Sure! Let's solve the system of linear equations step by step.
Given the system of equations:
[tex]\[
\begin{cases}
3x - 5y = 16 \\
2x + y = 15
\end{cases}
\][/tex]
### Step 1: Solve one of the equations for one variable
We can solve the second equation for [tex]\( y \)[/tex]:
[tex]\[
2x + y = 15 \implies y = 15 - 2x
\][/tex]
### Step 2: Substitute [tex]\( y \)[/tex] into the first equation
Now we'll substitute [tex]\( y = 15 - 2x \)[/tex] into the first equation:
[tex]\[
3x - 5(15 - 2x) = 16
\][/tex]
### Step 3: Simplify and solve for [tex]\( x \)[/tex]
Expand and simplify the equation:
[tex]\[
3x - 75 + 10x = 16 \implies 13x - 75 = 16 \implies 13x = 91 \implies x = \frac{91}{13}
\][/tex]
So,
[tex]\[
x = 7
\][/tex]
### Step 4: Substitute [tex]\( x \)[/tex] back to find [tex]\( y \)[/tex]
Now we use [tex]\( x = 7 \)[/tex] in the equation [tex]\( y = 15 - 2x \)[/tex]:
[tex]\[
y = 15 - 2(7) \implies y = 15 - 14 \implies y = 1
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
(x, y) = (7, 1)
\][/tex]
So the answer is:
[tex]\[
(x, y) = (7, 1)
\][/tex]
