Question

Solve the system of equations. 3x - 4y = 40
5x - 5y = 55

Answer 1

To solve the system of equations:

1. \( 3x - 4y = 40 \) (Equation 1)
2. \( 5x - 5y = 55 \) (Equation 2)

First, we can simplify Equation 2. Dividing every term by 5 gives us:

\[
x - y = 11 \tag{Equation 2 simplified}
\]

Next, we can express \( x \) in terms of \( y \) from Equation 2:

\[
x = y + 11 \tag{Equation 3}
\]

Now, we can substitute Equation 3 into Equation 1:

\[
3(y + 11) - 4y = 40
\]

Expanding this gives:

\[
3y + 33 - 4y = 40
\]

Combining like terms:

\[
-y + 33 = 40
\]

To isolate \( y \), we can subtract 33 from both sides:

\[
-y = 40 - 33
\]

\[
-y = 7
\]

Multiplying by -1 gives:

\[
y = -7
\]

Now, we can substitute \( y = -7 \) back into Equation 3 to find \( x \):

\[
x = -7 + 11
\]

\[
x = 4
\]

Now we have the solution:

\[
x = 4, \quad y = -7
\]

To verify, we can substitute these values into the original equations:

1. For Equation 1:
\[
3(4) - 4(-7) = 12 + 28 = 40 \quad \text{(True)}
\]

2. For Equation 2:
\[
5(4) - 5(-7) = 20 + 35 = 55 \quad \text{(True)}
\]

Thus, the solution to the system of equations is:

\[
\boxed{(4, -7)}
\]