Question

the first linear equation in a system has a slope of $-5$ and a y-intercept of 3. the second linear equation has a slope of $-3$ and passes through the point $(2, -1)$. what is the solution to the system of equations?
$(-1, 8)$
$(1, 8)$
$(2, 7)$
$(2, -7)$

Explanation:

Step1: Write first equation (slope-intercept)

Slope-intercept form is $y=mx+b$, where $m=-5$, $b=3$.
$y = -5x + 3$

Step2: Write second equation (point-slope)

Point-slope form: $y-y_1=m(x-x_1)$, $m=-3$, $(x_1,y_1)=(2,-1)$.
$y - (-1) = -3(x - 2)$
Simplify: $y + 1 = -3x + 6$, so $y = -3x + 5$

Step3: Set equations equal, solve for $x$

Set $-5x + 3 = -3x + 5$
Rearrange: $-5x + 3x = 5 - 3$
$-2x = 2$
$x = \frac{2}{-2} = -1$

Step4: Substitute $x=-1$ to find $y$

Use $y = -5x + 3$:
$y = -5(-1) + 3 = 5 + 3 = 8$

Answer:

(-1, 8)