Question

1. consider the system of equations.

$y = -\frac{1}{2}x + 6$
$y = 3x - 15$
to find the solution to the system of equations, a student plots points for both equations on a coordinate plane.
coordinate plane image
what is the solution to the system of equations?
a $(0, -8)$
b $(3, 6)$
c $(5, 0)$
d $(6, 3)$

Explanation:

Step1: Set equations equal

Since $y$ is equal to both expressions, set them equal to each other:
$$-\frac{1}{2}x + 6 = 3x - 15$$

Step2: Eliminate fraction, multiply all terms by 2

Multiply every term by 2 to remove the denominator:
$$-x + 12 = 6x - 30$$

Step3: Isolate x terms

Bring all $x$ terms to one side and constants to the other:
$$12 + 30 = 6x + x$$
$$42 = 7x$$

Step4: Solve for x

Divide both sides by 7 to find $x$:
$$x = \frac{42}{7} = 6$$

Step5: Find y using x=6

Substitute $x=6$ into $y=3x-15$:
$$y = 3(6) - 15 = 18 - 15 = 3$$

Answer:

D (6, 3)