Question

Find the solution of the system of equations.
minus, 5, x, plus, 7, y, equals, 40
−5x+7y=
40
10, x, plus, 7, y, equals, 25
10x+7y=
25
Answer
Attempt 1 out of 2

left parenthesis(
,
right parenthesis) Submit Answer

Answer 1

To solve the system of equations:

1. \(-5x + 7y = 40\) (Equation 1)
2. \(10x + 7y = 25\) (Equation 2)

We can use the elimination method to solve for \(x\) and \(y\).

First, we'll subtract Equation 1 from Equation 2 to eliminate \(y\):

\[
(10x + 7y) - (-5x + 7y) = 25 - 40
\]

Simplifying this gives:

\[
10x + 7y + 5x - 7y = -15
\]

Combine like terms:

\[
15x = -15
\]

Now, solve for \(x\):

\[
x = -1
\]

Next, we can substitute \(x = -1\) back into one of the original equations to find \(y\). We will use Equation 1:

\[
-5(-1) + 7y = 40
\]

This simplifies to:

\[
5 + 7y = 40
\]

Subtract 5 from both sides:

\[
7y = 35
\]

Now, divide by 7:

\[
y = 5
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-1, 5)
\]

So, the final answer is:

\[
\boxed{(-1, 5)}
\]