Question

solve the system of equations below.
$x + y = -4$
$y = 3x + 16$

a. $(-5, 1)$
b. $(10, -14)$
c. $(3, -7)$
d. $(4, -4)$

Explanation:

Step1: Substitute \( y = 3x + 16 \) into \( x + y = -4 \)

Substitute the expression for \( y \) from the second equation into the first equation. So we get \( x + (3x + 16) = -4 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side of the equation: \( x+3x + 16=-4 \), which combines to \( 4x+16=-4 \).
Subtract 16 from both sides: \( 4x=-4 - 16=-20 \).
Divide both sides by 4: \( x=\frac{-20}{4}=-5 \).

Step3: Substitute \( x = - 5 \) into \( y = 3x+16 \) to find \( y \)

Substitute \( x=-5 \) into \( y = 3x + 16 \), we have \( y=3\times(-5)+16=-15 + 16 = 1 \).

Answer:

A. \((-5,1)\)