Question

what is the value of x in the solution to this system of equations?
3x - 5y = 22

y = - 5x + 32

a - 6.5

b 0.5

c 6.5

d - 0.5

Explanation:

Step1: Substitute \( y = -5x + 32 \) into \( 3x - 5y = 22 \)

We know that \( y = -5x + 32 \), so we can replace \( y \) in the first equation with \( -5x + 32 \). This gives us:
\( 3x - 5(-5x + 32) = 22 \)

Step2: Simplify the equation

First, distribute the -5 in \( -5(-5x + 32) \):
\( 3x + 25x - 160 = 22 \)
Then, combine like terms (3x + 25x):
\( 28x - 160 = 22 \)

Step3: Solve for \( x \)

Add 160 to both sides of the equation:
\( 28x = 22 + 160 \)
\( 28x = 182 \)
Now, divide both sides by 28:
\( x = \frac{182}{28} = 6.5 \)

Answer:

C. 6.5