Question

Answer the questions and complete the steps to solve the system of equations below.
10х - 8y = -2
9х + 8y = 59

--
A)
variable y, because it has opposite coefficients
B)
Answer
19х = 57
C)
Answer
19х
57
＝.
Answer: 19
19
x = 3
D)
Answer
-
9x + 8y = 59
9(3) + 8y = 59
Answer: 27 + 8y = 59
8y = 32
У =4
E)
Answer
(3, 4)
F
Answer
10х - 8y = -2
9z + 8y= 59
10(3) - 8(4) = -2
9(3) + 8(4) = 59
Answer:
30 - 32 = -2
27 + 32 = 59
-2 = -2
59 = 59
::Use substitution to check your solution for the system. Show your work.
:: Which variable will you eliminate?
:: Solve the equation for x. Show your work.
# Substitute that value for x into either equation and solve for y. Show your work.
:: Write your solution as an ordered pair (x, y)
:: Add the two equations

Answer 1

Let’s solve the system of equations step by step, following the instructions provided. The equations given are:

1. \( 10x - 8y = -2 \) (Equation 1)
2. \( 9x + 8y = 59 \) (Equation 2)

### Which variable will you eliminate?

Since the coefficients of \( y \) in Equation 1 and Equation 2 are opposites (i.e., -8 and +8), we will eliminate variable \( y \).

### Add the two equations:

Adding Equation 1 and Equation 2:

\[
(10x - 8y) + (9x + 8y) = -2 + 59
\]

\[
10x + 9x - 8y + 8y = -2 + 59
\]

\[
19x = 57
\]

### Solve the equation for x. Show your work:

To find \( x \), divide both sides by 19:

\[
x = \frac{57}{19}
\]

Calculating gives:

\[
x = 3
\]

### Substitute that value for x into either equation and solve for y. Show your work:

Now we substitute \( x = 3 \) into one of the original equations. We can use Equation 2:

\[
9(3) + 8y = 59
\]

Calculating gives:

\[
27 + 8y = 59
\]

Now, subtract 27 from both sides:

\[
8y = 59 - 27
\]

\[
8y = 32
\]

Then divide both sides by 8:

\[
y = \frac{32}{8} = 4
\]

### Write your solution as an ordered pair (x, y):

The solution to the system of equations is:

\[
(x, y) = (3, 4)
\]

### Use substitution to check your solution for the system. Show your work:

We can verify the solution \( (3, 4) \) by substituting it back into both equations.

1. For Equation 1:

\[
10(3) - 8(4) = -2
\]

Calculating:

\[
30 - 32 = -2
\]

This is true, so Equation 1 holds.

2. For Equation 2:

\[
9(3) + 8(4) = 59
\]

Calculating:

\[
27 + 32 = 59
\]

This is also true, so Equation 2 holds.

### Final Answers:

The solution to the system is \( (3, 4) \).