Question

the first linear equation in a system has a slope of -4 and a y-intercept of 2. the second linear equation has a slope of -2 and passes through the point (3, -2). what is the solution to the system of equations?
(-1, 6)
(1, 6)
(0, 5)

Explanation:

Step1: Write first equation

The slope-intercept form is \( y = mx + b \), where \( m \) is slope and \( b \) is y-intercept. For first equation, \( m=-4 \), \( b = 2 \), so \( y=-4x + 2 \).

Step2: Write second equation

For second equation, \( m=-2 \), use point - slope form \( y - y_1=m(x - x_1) \) with \( (x_1,y_1)=(3,-2) \). Substitute values: \( y-(-2)=-2(x - 3) \), simplify to \( y + 2=-2x+6 \), then \( y=-2x + 4 \).

Step3: Solve the system

Set \( -4x + 2=-2x + 4 \). Add \( 4x \) to both sides: \( 2 = 2x+4 \). Subtract 4: \( -2 = 2x \), so \( x=-1 \). Substitute \( x = - 1 \) into \( y=-4x + 2 \): \( y=-4(-1)+2=4 + 2=6 \).

Answer:

\((-1,6)\)