Systems of Equations
Solve a System of Equations by Graphing
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Question 1 of 7
1. Question
Find the solution to the system of equations by graphing.
`x-3=0`
`x+y=1`
- `x=` (3) `y=` (-2)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `x-3=0`Make `x` the subject to get the equation of the line.`x-3 \ color(crimson)(+3)` `=` `0 \ color(crimson)(+3)` Add `3` to both sides `x \ cancel(-3) cancel(+3)` `=` `0 \ color(crimson)(+3)` `x` `=` `3` 
Graph: `x+y=1`First, make `y` the subject.`x+y` `=` `1` `y` `=` `-x+1` Make `y` the subject Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `1` `0` `-1` `-2` Plot the points and draw the graph.
The graphs intersect at the point `(3,-2)`
`:. color(darkviolet)(x=3, \ y=-2)``x=3, y=-2` -
Question 2 of 7
2. Question
Find the solution to the system of equations by graphing.
`2x+y=5`
`5x-3y=7`
- `x=` (2) `y=` (1)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `2x+y=5`Make `y` the subject to get the equation of the line.`2x+y \ color(crimson)(-2x)` `=` `5 \ color(crimson)(-2x)` Add `-2x` to both sides `y \ cancel(+2x) cancel(-2x)` `=` `5 \ color(crimson)(-2x)` `y` `=` `-2x+5` Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `5` `3` `1` `-1` Plot the points and draw the graph.
Graph: `5x-3y=7`First, make `y` the subject.`5x-3y` `=` `7` Make `y` the subject `-3y` `=` `-5x+7` Add `-5x` to both sides `y` `=` `5/3x-7/3` Divide both sides by `-3` Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `-7/3` `-2/3` `1` `8/3` Plot the points and draw the graph.
The graphs intersect at the point `(2,1)`
`:. color(darkviolet)(x=2, \ y=1)``x=2, y=1` -
Question 3 of 7
3. Question
Find the solution to the system of equations by graphing.
`4x-3y=1`
`3x+2y=5`
- `x=` (1) `y=` (1)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `4x-3y=1`Make `y` the subject to get the equation of the line.`4x-3y \ color(crimson)(-4x)` `=` `1 \ color(crimson)(-4x)` Add `-4x` to both sides `-3y \ cancel(+4x) cancel(-4x)` `=` `1 \ color(crimson)(-4x)` `\ color(crimson)(-3)y \ color(crimson)(\div(-3))` `=` `(-4x+1 )\ color(crimson)(\div(-3))` Divide both sides by `-3` `y` `=` `4/3x-1/3` Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `-1/3` `1` `7/3` `11/3` Plot the points and draw the graph.
Graph: `3x+2y=5`First, make `y` the subject.`3x+2y` `=` `5` Make `y` the subject `2y` `=` `-3x+5` Add `-3x` to both sides `y` `=` `-3/2x+5/2` Divide both sides by `2` Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `5/2` `1` `-1/2` `-2` Plot the points and draw the graph.
The graphs intersect at the point `(1,1)`
`:. color(darkviolet)(x=1, \ y=1)``x=1, y=1` -
Question 4 of 7
4. Question
Find the solution to the system of equations by graphing.
`x+3y=15`
`y-x=1`
- `x=` (3) `y=` (4)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `x+3y=15`Make `y` the subject to get the equation of the line.`x+3y \ color(crimson)(-x)` `=` `15 \ color(crimson)(-x)` Add `-x` to both sides `3y \ cancel(+x) cancel(-x)` `=` `15 \ color(crimson)(-x)` `\ color(crimson)(3)y\ color(crimson)(\div(3))` `=` `(-x+15) \ color(crimson)(\div(3))` Divide both sides by `3` `y` `=` `-1/3x+5` Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `5` `14/3` `13/3` `4` Plot the points and draw the graph.
Graph: `y-x=1`First, make `y` the subject.`y-x` `=` `1` `y` `=` `x+1` Make `y` the subject Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `1` `2` `3` `4` Plot the points and draw the graph.
The graphs intersect at the point `(3,4)`
`:. color(darkviolet)(x=3, \ y=4)``x=3, y=4` -
Question 5 of 7
5. Question
Find the solution to the system of equations by graphing.
`2x+y=2`
`x+y=2`
- `x=` (0) `y=` (2)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `2x+y=2`Make `y` the subject to get the equation of the line.`2x+y \ color(crimson)(-2x)` `=` `2 \ color(crimson)(-2x)` Add `-2x` to both sides `y \ cancel(+2x) cancel(-2x)` `=` `2\ color(crimson)(-2x)` `y` `=` `-2x+2` Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `2` `0` `-2` `-4` Plot the points and draw the graph.
Graph: `x+y=2`First, make `y` the subject.`x+y` `=` `2` `y` `=` `-x+2` Make `y` the subject Working out the y-values for each x-value in the table of values.`x` `0` `1` `2` `3` `y` `2` `1` `0` `-1` Plot the points and draw the graph.
The graphs intersect at the point `(0,2)`
`:. color(darkviolet)(x=0, \ y=2)``x=0, y=2` -
Question 6 of 7
6. Question
Find the solution to the system of equations by graphing.
`y-x=4`
`x-y=1`
- `x=` (no solution) `y=` (no solution)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `y-x=4`Make `y` the subject to get the equation of the line.`y-x \ color(crimson)(+x)` `=` `4 \ color(crimson)(+x)` Add `x` to both sides `y \ cancel(-x) cancel(+x)` `=` `4 \ color(crimson)(+x)` `y` `=` `x+4` Working out the y-values for each x-value in the table of values.`x` `-2` `0` `2` `4` `y` `2` `4` `6` `8` Plot the points and draw the graph.
Graph: `x+y=1`First, make `y` the subject.`x-y` `=` `1` `y` `=` `x-1` Make `y` the subject Working out the y-values for each x-value in the table of values.`x` `-2` `0` `2` `4` `y` `-3` `-1` `1` `3` Plot the points and draw the graph.
The graphs are parallel the lines do not intersect.There is no solution.There is no solution. -
Question 7 of 7
7. Question
Find the solution to the system of equations by graphing.
`-6x+2y=8`
`y=3x+4`
- `x=` (infinite solutions) `y=` (infinite solutions)
Correct
Great Work!
Incorrect
Help VideoFirst graph the equations.Graph: `-6x+2y=8`Make `y` the subject to get the equation of the line.`-6x+2y \ color(crimson)(+6x)` `=` `8 \ color(crimson)(+6x)` Add `6x` to both sides `2y \ cancel(-6x) cancel(+6x)` `=` `8 \ color(crimson)(+6x)` `\ color(crimson)(2)y\ color(crimson)(\div(2))` `=` `(6x+8) \ color(crimson)(\div(2))` Divide both sides by `2` `y` `=` `3x+4` Working out the y-values for each x-value in the table of values.`x` `-2` `-1` `0` `1` `y` `-2` `1` `4` `7` Plot the points and draw the graph.
Graph: `y=3x+4`First, `y` is the subject.`y` `=` `3x+4` `y` is the subject Working out the y-values for each x-value in the table of values.`x` `-2` `-1` `0` `1` `y` `-2` `1` `4` `7` Plot the points and draw the graph.
The graphs are both the same single line. This means there is an infinite number of solutions.Infinite solutionsInfinite solutions
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