Question

question 2 (multiple choice worth 2 points) (06.02r mc) solve the system $2x + 2y = -6$ and $3x - 2y = 11$ by using graph paper or graphing technology. what is the solution to the system? $(-1, -7)$ $(1, -4)$ $(2, -1)$ $(3, -2)$

Explanation:

Step1: Add the two equations to eliminate \( y \)

We have the system:

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Adding the left - hand sides and the right - hand sides of the two equations:
\((2x + 2y)+(3x - 2y)=-6 + 11\)
Simplify the left - hand side: \(2x+3x+2y - 2y=5x\), and the right - hand side: \(5\). So we get \(5x = 5\).

Step2: Solve for \( x \)

Divide both sides of the equation \(5x = 5\) by 5:
\(x=\frac{5}{5}=1\)

Step3: Substitute \( x = 1 \) into one of the original equations to solve for \( y \)

Let's substitute \( x = 1 \) into the first equation \(2x + 2y=-6\).
We have \(2(1)+2y=-6\)
Simplify the left - hand side: \(2 + 2y=-6\)
Subtract 2 from both sides: \(2y=-6 - 2=-8\)
Divide both sides by 2: \(y=\frac{-8}{2}=-4\)

Answer:

(1, -4)