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$y=y= 2x-2x ++ (-1)3 $ To graph these equations, we will start by plotting their $y-$intercepts. Then, we will use the slope to determine another point that satisfies each equation, and connect the points with a line.

We can see that the lines intersect at exactly one point.

It appears that the lines intersect at $(1,1).$ This is the solution to the system.

b

$3y+5x=6$

Write in slope-intercept form

SubEqn$LHS−5x=RHS−5x$

$3y=6−5x$

DivEqn$LHS/3=RHS/3$

$y=36−5x $

WriteDiffFracWrite as a difference of fractions

$y=36 −35x $

CalcQuotCalculate quotient

$y=2−35x $

CommutativePropAddCommutative Property of Addition

$y=-35x +2$

MovePartNumRight$ca⋅b =ca ⋅b$

$y=-35 x+2$

$x−3y=12$

Write in slope-intercept form

AddEqn$LHS+3y=RHS+3y$

$x=12+3y$

SubEqn$LHS−12=RHS−12$

$x−12=3y$

DivEqn$LHS/3=RHS/3$

$3x−12 =y$

RearrangeEqnRearrange equation

$y=3x−12 $

WriteDiffFracWrite as a difference of fractions

$y=3x −312 $

CalcQuotCalculate quotient

$y=3x −4$

MovePartNumRight$ca⋅b =ca ⋅b$

$y=31 x−4$

To graph these equations, we will start by plotting their $y$-intercepts. Then, we will use the slope to determine another point that satisfies each equation, and connect the points with a line.

We can see that the lines intersect at exactly one point.

It appears that the lines intersect at $(3,-3).$ This is the solution to the system.