Question

9x − 7y = 16
–8x + 5y = –13

Answer 1

To solve the system of equations:

1. \( 9x - 7y = 16 \) (Equation 1)
2. \( -8x + 5y = -13 \) (Equation 2)

We can use the substitution or elimination method. Here, we'll use the elimination method.

First, let's manipulate the equations to eliminate one of the variables. We can do this by finding a common coefficient for either \(x\) or \(y\). Let's eliminate \(y\).

To make the coefficients of \(y\) the same, we can multiply Equation 1 by 5 and Equation 2 by 7:

1. \(5(9x - 7y) = 5(16)\)
\[
45x - 35y = 80 \quad (Equation 3)
\]

2. \(7(-8x + 5y) = 7(-13)\)
\[
-56x + 35y = -91 \quad (Equation 4)
\]

Now we can add Equation 3 and Equation 4 to eliminate \(y\):

\[
(45x - 35y) + (-56x + 35y) = 80 + (-91)
\]

This simplifies to:

\[
-11x = -11
\]

Now, divide both sides by -11:

\[
x = 1
\]

Now that we have \(x\), we can substitute \(x = 1\) back into one of the original equations to find \(y\). Let's use Equation 1:

\[
9(1) - 7y = 16
\]
\[
9 - 7y = 16
\]
\[
-7y = 16 - 9
\]
\[
-7y = 7
\]
\[
y = -1
\]

Thus, the solution to the system of equations is:

\[
x = 1, \quad y = -1
\]

In ordered pair form, the solution is \((1, -1)\).