Question

find the solution of the system of equations.\

$$\begin{cases}2x + 2y = 10\\\\5x + 2y = 10\\end{cases}$$

\
show your work here\
x = \
y =

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 2x + 2y = 10 \\ 5x + 2y = 10 \end{cases}$$

Subtract the first equation from the second equation: $(5x + 2y)-(2x + 2y)=10 - 10$.
Simplify the left - hand side: $5x+2y - 2x - 2y=3x$, and the right - hand side is $0$. So we get $3x = 0$.

Step2: Solve for x

From $3x=0$, divide both sides by 3: $x=\frac{0}{3}=0$.

Step3: Substitute x into one of the original equations

Substitute $x = 0$ into the first equation $2x+2y = 10$. We get $2\times0+2y=10$, which simplifies to $2y = 10$.

Step4: Solve for y

Divide both sides of $2y = 10$ by 2: $y=\frac{10}{2}=5$.

Answer:

$x = 0$, $y = 5$