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 two equations equal

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

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( 4x + 2x + 2 = -4 \) which simplifies to \( 6x + 2 = -4 \). Then subtract 2 from both sides: \( 6x = -4 - 2 = -6 \). Divide both sides by 6: \( x = \frac{-6}{6} = -1 \).

Step3: Find \( y \) by substituting \( x = -1 \) into one of the equations

Using \( y = 4x + 2 \), substitute \( x = -1 \): \( y = 4(-1) + 2 = -4 + 2 = -2 \). So the solution is \( (-1, -2) \), meaning there is 1 solution.

Answer:

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