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)
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First 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

Find the solution to the system of equations by graphing.

$2x+y=5$

$5x-3y=7$

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

Question 3 of 7

Find the solution to the system of equations by graphing.

$4x-3y=1$

$3x+2y=5$

$x=$ (1) $y=$ (1)

Question 4 of 7

Find the solution to the system of equations by graphing.

$x+3y=15$

$y-x=1$

$x=$ (3) $y=$ (4)

Question 5 of 7

Find the solution to the system of equations by graphing.

$2x+y=2$

$x+y=2$

$x=$ (0) $y=$ (2)

Question 6 of 7

Find the solution to the system of equations by graphing.

$y-x=4$

$x-y=1$

$x=$ (no solution) $y=$ (no solution)

Question 7 of 7

Find the solution to the system of equations by graphing.

$-6x+2y=8$

$y=3x+4$

$x=$ (infinite solutions) $y=$ (infinite solutions)

$2x+y \ color(crimson)(-2x)$	$=$	$5 \ color(crimson)(-2x)$	Add $-2x$ to both sides
$y \ cancel(+2x) cancel(-2x)$	$=$	$5 \ color(crimson)(-2x)$
$y$	$=$	$-2x+5$

$5x-3y$	$=$	$7$	Make $y$ the subject
$-3y$	$=$	$-5x+7$	Add $-5x$ to both sides
$y$	$=$	$5/3x-7/3$	Divide both sides by $-3$

$4x-3y \ color(crimson)(-4x)$	$=$	$1 \ color(crimson)(-4x)$	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 $-3$
$y$	$=$	$4/3x-1/3$

$3x+2y$	$=$	$5$	Make $y$ the subject
$2y$	$=$	$-3x+5$	Add $-3x$ to both sides
$y$	$=$	$-3/2x+5/2$	Divide both sides by $2$

$x+3y \ color(crimson)(-x)$	$=$	$15 \ color(crimson)(-x)$	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 $3$
$y$	$=$	$-1/3x+5$

Solve a System of Equations by Graphing

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Quizzes

$x-3 \ color(crimson)(+3)$	$=$	$0 \ color(crimson)(+3)$	Add $3$ to both sides
$x \ cancel(-3) cancel(+3)$	$=$	$0 \ color(crimson)(+3)$
$x$	$=$	$3$

$2x+y \ color(crimson)(-2x)$	$=$	$2 \ color(crimson)(-2x)$	Add $-2x$ to both sides
$y \ cancel(+2x) cancel(-2x)$	$=$	$2\ color(crimson)(-2x)$
$y$	$=$	$-2x+2$

$y-x \ color(crimson)(+x)$	$=$	$4 \ color(crimson)(+x)$	Add $x$ to both sides
$y \ cancel(-x) cancel(+x)$	$=$	$4 \ color(crimson)(+x)$
$y$	$=$	$x+4$

$-6x+2y \ color(crimson)(+6x)$	$=$	$8 \ color(crimson)(+6x)$	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 $2$
$y$	$=$	$3x+4$

$x$	$0$	$1$	$2$	$3$
$y$	$1$	$0$	$-1$	$-2$

$x$	$0$	$1$	$2$	$3$
$y$	$-7/3$	$-2/3$	$1$	$8/3$

$x$	$0$	$1$	$2$	$3$
$y$	$-1/3$	$1$	$7/3$	$11/3$

$x$	$0$	$1$	$2$	$3$
$y$	$5/2$	$1$	$-1/2$	$-2$