Elimination Method 1

Question 2 of 6

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

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

$x - y = 3$ $x-y=3$
- $x =$ $x=$ (1)
  
  $y =$ $y=$ (-2)
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Elimination Method

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

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

$3)$ $3)$ solve for the variable that remains

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

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

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

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

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

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

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

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

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

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

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

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

Solve for $y$ $y$ from the difference.

$- y$ $-y$ $=$ $=$ $2$ $2$

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

$y$ $y$ $=$ $=$ $- 2$ $-2$

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

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

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

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

$x$ $x$ $=$ $=$ $1$ $1$

$x = 1, y = - 2$ $x=1, y =-2$

Question 3 of 6

Solve the following systems of equations by elimination.

5 x + 2 y = 25

$5x+2y=25$

4 x - 3 y = - 3

$4x-3y=-3$

$x =$ $x=$ (3)

$y =$ $y=$ (5)

Question 4 of 6

Solve the following systems of equations by elimination.

2 x - 7 y = 19

$2x-7y=19$

x + 2 y = 4

$x+2y=4$

$x =$ $x=$ (6)

$y =$ $y=$ (-1)

Question 5 of 6

Solve the following systems of equations by elimination.

2 x + y = - 5

$2x+y=-5$

4 x - 3 y = 5

$4x-3y=5$

$x =$ $x=$ (-1)

$y =$ $y=$ (-3)

Question 6 of 6

Solve the following systems of equations by elimination.

2 x - 4 y = - 4

$2x-4y=-4$

3 x - 2 y = - 10

$3x-2y=-10$

$x =$ $x=$ (-4)

$y =$ $y=$ (-1)

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Elimination Method

$1)$ $1)$ make sure a variable has same coefficients on the 2 equations
$2)$ $2)$ add or subtract the equations so that one variable is cancelled
$3)$ $3)$ solve for the variable that remains
$4)$ $4)$ substitute known value to one of the equations to solve for the other variable

First, label the two equations

1

$1$ and

2

$2$ respectively.

$2 x - 4 y$ $2x-4y$	$=$ $=$	$- 4$ $-4$	Equation $1$ $1$
$3 x - 2 y$ $3x-2y$	$=$ $=$	$- 10$ $-10$	Equation $2$ $2$

Next, multiply the values of equation

1

$1$ by

3

$3$ and label the product as equation

3

$3$ .

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

Also multiply the values of equation

2

$2$ by

2

$2$ and label the product as equation

4

$4$ .

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

Then, subtract equation

4

$4$ from equation

3

$3$ .

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

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

Solve for $y$ $y$ from the difference.

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

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

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

x = - 4, y = - 1

$x=-4, y =-1$

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

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

$15 x + 6 y$ $15x+6y$	$=$ $=$	$75$ $75$
$8 x - 6 y$ $8x-6y$	$=$ $=$	$- 6$ $-6$

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

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

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

Elimination Method 1

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Elimination Method

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Elimination Method

Quizzes

$2 x - 3 y$ $2x-3y$	$=$ $=$	$3$ $3$	Equation $1$ $1$
$4 x + 3 y$ $4x+3y$	$=$ $=$	$15$ $15$	Equation $2$ $2$

$6 x$ $6x$	$=$ $=$	$18$ $18$
$x$ $x$	$=$ $=$	$3$ $3$	Divide both sides by $6$ $6$

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

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

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

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

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

$11 x$ $11x$	$=$ $=$	$66$ $66$
$x$ $x$	$=$ $=$	$6$ $6$	Divide both sides by $11$ $11$

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

$2 x + y$ $2x+y$	$=$ $=$	$- 5$ $-5$	Equation $1$ $1$
$4 x - 3 y$ $4x-3y$	$=$ $=$	$5$ $5$	Equation $2$ $2$

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

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