Question

50x+50y=800
65x+75y=1100

solve for x

Answer 1

To solve the system of equations:

1. \( 50x + 50y = 800 \)
2. \( 65x + 75y = 1100 \)

We can start by simplifying the first equation. Divide the entire equation by 50:

\[
x + y = 16 \quad \text{(Equation 1)}
\]

Now we can express \(y\) in terms of \(x\):

\[
y = 16 - x \quad \text{(Substitution)}
\]

Now, substitute \(y\) into the second equation:

\[
65x + 75(16 - x) = 1100
\]

Distributing \(75\):

\[
65x + 1200 - 75x = 1100
\]

Combine like terms:

\[
-10x + 1200 = 1100
\]

Subtract \(1200\) from both sides:

\[
-10x = -100
\]

Dividing by \(-10\):

\[
x = 10
\]

So, the solution for \(x\) is:

\[
\boxed{10}
\]

To find \(y\), substitute \(x\) back into the equation \(y = 16 - x\):

\[
y = 16 - 10 = 6
\]

Thus, the complete solution is \(x = 10\) and \(y = 6\).