Question

multiple choice 1 point
which ordered pair is a solution to the system of linear equations -4x + y = 8 and x - 5y = 17?
a) (-3, -4) b) (-4, -3)
c) (-4, 3) d) (-3, 4)
a
b
c
d
clear my selection
7 multiple choice 1 point

Explanation:

Step1: Isolate $y$ from first equation

From $-4x + y = 8$, rearrange to get:
$y = 4x + 8$

Step2: Substitute $y$ into second equation

Substitute $y=4x+8$ into $x - 5y = 17$:
$x - 5(4x + 8) = 17$
Expand and simplify:
$x - 20x - 40 = 17$
$-19x = 17 + 40$
$-19x = 57$
$x = \frac{57}{-19} = -3$

Step3: Solve for $y$ using $x=-3$

Substitute $x=-3$ into $y=4x+8$:
$y = 4(-3) + 8 = -12 + 8 = -4$

Step4: Verify the solution

Check $(-3,-4)$ in both equations:

1. $-4(-3) + (-4) = 12 - 4 = 8$ (matches first equation)
2. $-3 - 5(-4) = -3 + 20 = 17$ (matches second equation)

Answer:

a) (-3, -4)