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Systems of Equations>
Solve a System of Equations by Graphing>
Solve a System of Equations by GraphingSolve 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.
`x3=0`
`x+y=1`
 `x=` (3) `y=` (2)
Correct
Great Work!
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First graph the equations.Graph: `x3=0`Make `x` the subject to get the equation of the line.`x3 \ 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 yvalues for each xvalue 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`
`5x3y=7`
 `x=` (2) `y=` (1)
Correct
Great Work!
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First 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 yvalues for each xvalue in the table of values.`x` `0` `1` `2` `3` `y` `5` `3` `1` `1` Plot the points and draw the graph.Graph: `5x3y=7`First, make `y` the subject.`5x3y` `=` `7` Make `y` the subject `3y` `=` `5x+7` Add `5x` to both sides `y` `=` `5/3x7/3` Divide both sides by `3` Working out the yvalues for each xvalue 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.
`4x3y=1`
`3x+2y=5`
 `x=` (1) `y=` (1)
Correct
Great Work!
Incorrect
First graph the equations.Graph: `4x3y=1`Make `y` the subject to get the equation of the line.`4x3y \ 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` `=` `4/3x1/3` Working out the yvalues for each xvalue 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 yvalues for each xvalue 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`
`yx=1`
 `x=` (3) `y=` (4)
Correct
Great Work!
Incorrect
First 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 yvalues for each xvalue 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: `yx=1`First, make `y` the subject.`yx` `=` `1` `y` `=` `x+1` Make `y` the subject Working out the yvalues for each xvalue 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
First 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 yvalues for each xvalue 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 yvalues for each xvalue 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.
`yx=4`
`xy=1`
 `x=` (no solution) `y=` (no solution)
Correct
Great Work!
Incorrect
First graph the equations.Graph: `yx=4`Make `y` the subject to get the equation of the line.`yx \ 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 yvalues for each xvalue 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.`xy` `=` `1` `y` `=` `x1` Make `y` the subject Working out the yvalues for each xvalue 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
First 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 yvalues for each xvalue 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 yvalues for each xvalue 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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