Question

solve the system of equations graphed on the coordinate axes below.
$y = -dfrac{1}{4}x - 6$
$y = 3x + 7$

Explanation:

Step1: Set the equations equal

Since both equations are solved for \( y \), set them equal: \( -\frac{1}{4}x - 6 = 3x + 7 \)

Step2: Multiply by 4 to eliminate fraction

Multiply each term by 4: \( -x - 24 = 12x + 28 \)

Step3: Move x terms to one side

Add \( x \) to both sides: \( -24 = 13x + 28 \)

Step4: Move constant terms

Subtract 28 from both sides: \( -52 = 13x \)

Step5: Solve for x

Divide by 13: \( x = -4 \)

Step6: Substitute x into one equation

Use \( y = 3x + 7 \), substitute \( x = -4 \): \( y = 3(-4) + 7 = -12 + 7 = -5 \)

Answer:

The solution to the system is \( x = -4 \), \( y = -5 \) or the ordered pair \( (-4, -5) \)