Question

Solve the system by substitution.
10, x, plus, 7, y, equals, minus, 41
10x+7y=
−41
minus, 4, x, plus, 7, equals, y
−4x+7=
y

Answer 1

To solve the system of equations by substitution, we first rewrite the equations given in a standard form:

1. \( 10x + 7y = -41 \) (Equation 1)
2. \( y = -4x + 7 \) (Equation 2)

Since Equation 2 already expresses \( y \) in terms of \( x \), we can substitute this expression for \( y \) into Equation 1.

**Substituting Equation 2 into Equation 1:**

\[
10x + 7(-4x + 7) = -41
\]

Now, distribute the 7:
\[
10x - 28x + 49 = -41
\]

Combine the \( x \) terms:
\[
-18x + 49 = -41
\]

Next, isolate the term with \( x \) by subtracting 49 from both sides:
\[
-18x = -41 - 49
\]
\[
-18x = -90
\]

Now, divide both sides by -18 to solve for \( x \):
\[
x = \frac{-90}{-18} = 5
\]

Now that we have \( x = 5 \), we can substitute this value back into Equation 2 to find \( y \):
\[
y = -4(5) + 7
\]
\[
y = -20 + 7
\]
\[
y = -13
\]

The solution to the system of equations is:
\[
x = 5, \quad y = -13
\]

Thus, the solution is:
\[
(x, y) = (5, -13)
\]