Question

1. maria wrote the following system on the board. 2x + 3y = 6 6x + 3y = -6 what is the solution to the system she wrote? (4,-3) (-3,4) (-4,3) (-3,-4)

Explanation:

Step1: Subtract second equation from first

Subtract $2x + 3y=6$ from $6x + 3y=-6$.
$(6x + 3y)-(2x + 3y)=-6 - 6$
$6x+3y - 2x - 3y=-12$
$4x=-12$

Step2: Solve for x

Divide both sides by 4.
$x=\frac{-12}{4}=-3$

Step3: Substitute x into second equation

Substitute $x = - 3$ into $2x+3y = 6$.
$2\times(-3)+3y=6$
$-6 + 3y=6$

Step4: Solve for y

Add 6 to both sides and then divide by 3.
$3y=6 + 6=12$
$y=\frac{12}{3}=4$

Answer:

$(-3,4)$