Elimination Method 1

Topics

Algebra 1

Systems of Equations

Elimination Method

Elimination Method 1

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 6

1. Question
Solve the following systems of equations by elimination.

$2x-3y=3$

$4x+3y=15$
- $x=$ (3)
  
  $y=$ (1)
Hint

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

In the elimination method you either add or subtract the equations to get the value of $x$ and $y$

First, label the two equations $1$ and $2$ respectively.

$2x-3y$ $=$ $3$ Equation $1$

$4x+3y$ $=$ $15$ Equation $2$

Next, add the two equations.

$2x-3y$ $=$ $3$

$4x+3y$ $=$ $15$

$6x$ $=$ $18$ $-3y+3y$ cancels out

Solve for $x$ .

$6x$ $=$ $18$

$x$ $=$ $3$ Divide both sides by $6$

Now, substitute the value of $x$ into any of the two equations.

$2$ $x$ $-3y$ $=$ $3$ Equation $1$

$2$ $(3)$ $-3y$ $=$ $3$ $x=3$

$6-3y$ $=$ $3$ Simplify

$6-3y$ $-6$ $=$ $3$ $-6$ Subtract $6$ from both sides

$-3y$ $=$ $-3$

$y$ $=$ $-1$

$x=3, y =1$
Question 2 of 6

2. Question
Solve the following systems of equations by elimination.

$2x-3y=8$

$x-y=3$
- $x=$ (1)
  
  $y=$ (-2)
Hint

Help Video
Correct

Nice Job!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Elimination Method

$1)$ make sure a variable has same coefficients on the 2 equations

$2)$ add or subtract the equations so that one variable is cancelled

$3)$ solve for the variable that remains

$4)$ substitute known value to one of the equations to solve for the other variable

First, label the two equations $1$ and $2$ respectively.

$2x-3y$ $=$ $8$ Equation $1$

$x-y$ $=$ $3$ Equation $2$

Next, multiply the values of equation $2$ by $2$ and label the product as equation $3$ .

$x-y$ $=$ $3$ Equation $2$

$(x-y)$ $times2$ $=$ $3$ $times2$ Multiply the values of both sides by $2$

$2x-2y$ $=$ $6$ Equation $3$

Then, subtract equation $3$ from equation $1$ .

$2x-3y$ $=$ $8$

$-$ $(2x-2y)$ $=$ $6$

$-y$ $=$ $2$ $2x-2x$ cancels out

Solve for $y$ from the difference.

$-y$ $=$ $2$

$-y$ $div(-1)$ $=$ $2$ $div(-1)$ Divide both sides by $-1$

$y$ $=$ $-2$

Now, substitute the value of $y$ into any of the two equations.

$x-$ $y$ $=$ $3$ Equation $2$

$x-$ $(-2)$ $=$ $3$ $y=-2$

$x+2$ $-2$ $=$ $3$ $-2$ Subtract $2$ from both sides

$x$ $=$ $1$

$x=1, y =-2$
Question 3 of 6

3. Question
Solve the following systems of equations by elimination.

$5x+2y=25$

$4x-3y=-3$
- $x=$ (3)
  
  $y=$ (5)
Hint

Help Video
Correct

Excellent!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

In the elimination method you either add or subtract the equations to get the value of $x$ and $y$

First, label the two equations $1$ and $2$ respectively.

$5x+2y$ $=$ $25$ Equation $1$

$4x-3y$ $=$ $-3$ Equation $2$

Multiply Equation $1$ by $3$ .

$5x+2y$ $=$ $25$

$(5x+2y)$ $xx 3$ $=$ $25$ $xx 3$

$15x+6y$ $=$ $75$ Simplify

Multiply Equation $2$ by $2$ .

$4x-3y$ $=$ $-3$

$(4x-3y)$ $xx 2$ $=$ $-3$ $xx 2$

$8x-6y$ $=$ $-6$ Simplify

Add the two transformed equations.

$15x+6y$ $=$ $75$

$8x-6y$ $=$ $-6$

$23x$ $=$ $69$ $6y-6y$ cancels out

Solve for $x$ .

$23x$ $=$ $69$

$x$ $=$ $3$ Divide both sides by $23$

Now, substitute the value of $x$ into any of the two equations.

$5$ $x$ $+2y$ $=$ $25$ Equation $1$

$5$ $(3)$ $+2y$ $=$ $25$ $x=3$

$15+2y$ $=$ $25$

$15+2y$ $-15$ $=$ $25$ $-15$ Subtract $15$ from both sides

$2y$ $=$ $10$

$y$ $=$ $5$ Divide both sides by $2$

$x=3, y =5$

Question 4 of 6

Solve the following systems of equations by elimination.

$2x-7y=19$

$x+2y=4$

$x=$ (6)

$y=$ (-1)

Question 5 of 6

Solve the following systems of equations by elimination.

$2x+y=-5$

$4x-3y=5$

$x=$ (-1)

$y=$ (-3)

Question 6 of 6

6. Question
Solve the following systems of equations by elimination.

$2x-4y=-4$

$3x-2y=-10$
- $x=$ (-4)
  
  $y=$ (-1)
Hint

Help Video
Correct

Exceptional!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Elimination Method

$1)$ make sure a variable has same coefficients on the 2 equations

$2)$ add or subtract the equations so that one variable is cancelled

$3)$ solve for the variable that remains

$4)$ substitute known value to one of the equations to solve for the other variable

First, label the two equations $1$ and $2$ respectively.

$2x-4y$ $=$ $-4$ Equation $1$

$3x-2y$ $=$ $-10$ Equation $2$

Next, multiply the values of equation $1$ by $3$ and label the product as equation $3$ .

$2x-4y$ $=$ $-4$ Equation $1$

$(2x-4y)$ $times3$ $=$ $-4$ $times3$ Multiply the values of both sides by $3$

$6x-12y$ $=$ $-12$ Equation $3$

Also multiply the values of equation $2$ by $2$ and label the product as equation $4$ .

$3x-2y$ $=$ $-10$ Equation $2$

$(3x-2y)$ $times2$ $=$ $-10$ $times2$ Multiply the values of both sides by $2$

$6x-4y$ $=$ $-20$ Equation $4$

Then, subtract equation $4$ from equation $3$ .

$6x-12y$ $=$ $-12$

$-$ $(6x-4y)$ $=$ $-20$

$-8y$ $=$ $8$ $6x-6x$ cancels out

Solve for $y$ from the difference.

$-8y$ $=$ $8$

$-8y$ $div(-8)$ $=$ $8$ $div(-8)$ Divide both sides by $-8$

$y$ $=$ $-1$

Now, substitute the value of $y$ into any of the two equations.

$2x-4$ $y$ $=$ $-4$ Equation $1$

$2x-4$ $(-1)$ $=$ $-4$ $y=-1$

$2x+4$ $-4$ $=$ $-4$ $-4$ Subtract $4$ from both sides

$2x$ $div2$ $=$ $-8$ $div2$ Divide both sides by $2$

$x$ $=$ $-4$

$x=-4, y =-1$

$2x-7y$	$=$	$19$
$(2x-7y)$ $xx 2$	$=$	$19$ $xx 2$
$4x-14y$	$=$	$38$	Simplify

$4x-14y$	$=$	$38$
$7x+14y$	$=$	$28$

$11x$	$=$	$66$	$-14y+14y$ cancels out

$2$ $x$ $-7y$	$=$	$19$	Equation $1$
$2$ $(6)$ $-7y$	$=$	$19$	$x=6$
$12-7y$	$=$	$19$
$12-7y$ $-12$	$=$	$19$ $-12$	Subtract $12$ from both sides
$-7y$	$=$	$7$
$y$	$=$	$-1$	Divide both sides by $-7$

Elimination Method 1

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Well Done!

2. Question

Hint

Nice Job!

Elimination Method

3. Question

Hint

Excellent!

4. Question

Hint

Well Done!

5. Question

Hint

Fantastic!

Elimination Method

6. Question

Hint

Exceptional!

Elimination Method

Quizzes

$2$ $x$ $-3y$	$=$	$3$	Equation $1$
$2$ $(3)$ $-3y$	$=$	$3$	$x=3$
$6-3y$	$=$	$3$	Simplify
$6-3y$ $-6$	$=$	$3$ $-6$	Subtract $6$ from both sides
$-3y$	$=$	$-3$
$y$	$=$	$-1$

$x-y$	$=$	$3$	Equation $2$
$(x-y)$ $times2$	$=$	$3$ $times2$	Multiply the values of both sides by $2$
$2x-2y$	$=$	$6$	Equation $3$

$2x-3y$	$=$	$8$
$-$ $(2x-2y)$	$=$	$6$

$-y$	$=$	$2$	$2x-2x$ cancels out

$-y$	$=$	$2$
$-y$ $div(-1)$	$=$	$2$ $div(-1)$	Divide both sides by $-1$
$y$	$=$	$-2$

$x-$ $y$	$=$	$3$	Equation $2$
$x-$ $(-2)$	$=$	$3$	$y=-2$
$x+2$ $-2$	$=$	$3$ $-2$	Subtract $2$ from both sides
$x$	$=$	$1$

$5x+2y$	$=$	$25$
$(5x+2y)$ $xx 3$	$=$	$25$ $xx 3$
$15x+6y$	$=$	$75$	Simplify

$4x-3y$	$=$	$-3$
$(4x-3y)$ $xx 2$	$=$	$-3$ $xx 2$
$8x-6y$	$=$	$-6$	Simplify

$5$ $x$ $+2y$	$=$	$25$	Equation $1$
$5$ $(3)$ $+2y$	$=$	$25$	$x=3$
$15+2y$	$=$	$25$
$15+2y$ $-15$	$=$	$25$ $-15$	Subtract $15$ from both sides
$2y$	$=$	$10$
$y$	$=$	$5$	Divide both sides by $2$

$x+2y$	$=$	$4$
$(x+2y)$ $xx 7$	$=$	$4$ $xx 7$
$7x+14y$	$=$	$28$	Simplify

$2x+y$	$=$	$-5$	Equation $1$
$(2x+y)$ $times3$	$=$	$-5$ $times3$	Multiply the values of both sides by $3$
$6x+3y$	$=$	$-15$	Equation $3$

$4x-3y$	$=$	$5$
$+$ $(6x+3y)$	$=$	$-15$

$10x$	$=$	$-10$	$-3y+3y$ cancels out

$10x$	$=$	$-10$
$10x$ $div10$	$=$	$-10$ $div10$	Divide both sides by $10$
$x$	$=$	$-1$

$4$ $x$ $-3y$	$=$	$5$	Equation $2$
$4$ $(-1)$ $-3y$	$=$	$5$	$x=-1$
$-4-3y$ $+4$	$=$	$5$ $+4$	Add $4$ to both sides
$-3y$ $div(-3)$	$=$	$9$ $div(-3)$	Divide both sides by $-3$
$y$	$=$	$-3$

$2x-4y$	$=$	$-4$	Equation $1$
$(2x-4y)$ $times3$	$=$	$-4$ $times3$	Multiply the values of both sides by $3$
$6x-12y$	$=$	$-12$	Equation $3$

$3x-2y$	$=$	$-10$	Equation $2$
$(3x-2y)$ $times2$	$=$	$-10$ $times2$	Multiply the values of both sides by $2$
$6x-4y$	$=$	$-20$	Equation $4$

$6x-12y$	$=$	$-12$
$-$ $(6x-4y)$	$=$	$-20$

$-8y$	$=$	$8$	$6x-6x$ cancels out

$-8y$	$=$	$8$
$-8y$ $div(-8)$	$=$	$8$ $div(-8)$	Divide both sides by $-8$
$y$	$=$	$-1$

$2x-4$ $y$	$=$	$-4$	Equation $1$
$2x-4$ $(-1)$	$=$	$-4$	$y=-1$
$2x+4$ $-4$	$=$	$-4$ $-4$	Subtract $4$ from both sides
$2x$ $div2$	$=$	$-8$ $div2$	Divide both sides by $2$
$x$	$=$	$-4$