Question

graph the system on a separate sheet of paper and determine the number of solutions it has. if it has one solution, determine its coordinates.
$y = 4x + 2$
$y = -2x - 4$
a) infinitely many solutions
b) 1 solution; $(-1, 0)$
c) no solution
d) 1 solution; $(-1, -2)$

Explanation:

Step1: Set the equations equal

Since both equations are solved for \( y \), set \( 4x + 2=-2x - 4 \).

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( 4x+2x + 2=-2x+2x - 4\) → \( 6x + 2=-4 \).
Subtract 2 from both sides: \( 6x+2 - 2=-4 - 2\) → \( 6x=-6 \).
Divide by 6: \( x=\frac{-6}{6}=-1 \).

Step3: Find \( y \)

Substitute \( x = - 1 \) into \( y = 4x+2 \): \( y = 4(-1)+2=-4 + 2=-2 \).

Answer:

D) 1 solution; \((-1, -2)\)