Question

solve each system by any method.

1. ( y = 4x + 21 )

( -5x - 7y = 18 )
a) ( (5, 1) ) b) ( (-5, -1) )
c) ( (-5, 1) ) d) no solution

Explanation:

Step1: Substitute \( y = 4x + 21 \) into the second equation

We have the second equation \( -5x - 7y = 18 \). Substitute \( y \) with \( 4x + 21 \):
\( -5x - 7(4x + 21) = 18 \)

Step2: Simplify and solve for \( x \)

First, expand the left - hand side:
\( -5x-28x - 147 = 18 \)
Combine like terms:
\( -33x-147 = 18 \)
Add 147 to both sides:
\( -33x=18 + 147 \)
\( -33x=165 \)
Divide both sides by - 33:
\( x=\frac{165}{-33}=-5 \)

Step3: Find the value of \( y \)

Substitute \( x = - 5 \) into \( y = 4x+21 \):
\( y=4\times(-5)+21=-20 + 21 = 1 \)

Answer:

C) \((-5,1)\)