find the solution of the system of equations.

$-2x - 2y = -28$

$2x + 4y = 42$

Question

find the solution of the system of equations.

$-2x - 2y = -28$

$2x + 4y = 42$

Accepted Answer

# Explanation:
## Step1: Add the two equations to eliminate $x$
The first equation is $-2x - 2y = -28$ and the second is $2x + 4y = 42$. When we add them together:
$$
\begin{align*}
(-2x - 2y)+(2x + 4y)&=-28 + 42\
-2x - 2y+2x + 4y&=14\
2y&=14
\end{align*}
$$
## Step2: Solve for $y$
Divide both sides of $2y = 14$ by 2:
$$
y=\frac{14}{2}=7
$$
## Step3: Substitute $y = 7$ into one of the original equations to find $x$
Let's use the second equation $2x + 4y = 42$. Substitute $y = 7$:
$$
\begin{align*}
2x+4\times7&=42\
2x + 28&=42\
2x&=42 - 28\
2x&=14\
x&=\frac{14}{2}=7
\end{align*}
$$
# Answer:
The solution of the system of equations is $x = 7$ and $y = 7$ (or in ordered pair form $(7, 7)$).

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QUESTION IMAGE

Question

Explanation:

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

Step2: Solve for \(y\)

Step3: Substitute \(y = 7\) into one of the original equations to find \(x\)

Answer: