Certainly! Let's solve the given system of linear equations step-by-step:
[tex]\[
\begin{cases}
2x + 3y = 5 \\
2x - y = -7
\end{cases}
\][/tex]
### Step 1: Express [tex]\( y \)[/tex] from the second equation.
First, we solve the second equation for [tex]\( y \)[/tex]:
[tex]\[
2x - y = -7
\][/tex]
Rearrange to solve for [tex]\( y \)[/tex]:
[tex]\[
-y = -7 - 2x
\][/tex]
Multiply by [tex]\(-1\)[/tex] to isolate [tex]\( y \)[/tex]:
[tex]\[
y = 7 + 2x
\][/tex]
### Step 2: Substitute [tex]\( y \)[/tex] into the first equation.
Now we substitute [tex]\( y = 7 + 2x \)[/tex] into the first equation:
[tex]\[
2x + 3(7 + 2x) = 5
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex].
Distribute the 3 in the equation:
[tex]\[
2x + 21 + 6x = 5
\][/tex]
Combine like terms:
[tex]\[
8x + 21 = 5
\][/tex]
Subtract 21 from both sides:
[tex]\[
8x = 5 - 21
\][/tex]
[tex]\[
8x = -16
\][/tex]
Divide by 8:
[tex]\[
x = -2
\][/tex]
### Step 4: Solve for [tex]\( y \)[/tex].
Substitute [tex]\( x = -2 \)[/tex] back into the equation for [tex]\( y \)[/tex]:
[tex]\[
y = 7 + 2(-2)
\][/tex]
Simplify:
[tex]\[
y = 7 - 4
\][/tex]
[tex]\[
y = 3
\][/tex]
### Solution
The solution to the system of equations is:
[tex]\[
(x, y) = (-2, 3)
\][/tex]
