Question

which ordered pair is the solution to the system of linear equations -5x + y = -26 and 2x - 7y = -16 ?
a) (6, -4) b) (-4, -6)
c) (-4, 6) d) (-6, -4)
a
b
c
d
clear my selection

Explanation:

Step1: Isolate y from first equation

From $-5x + y = 26$, we get $y = 5x + 26$.

Step2: Substitute y into second equation

Substitute $y = 5x + 26$ into $2x - 7y = 16$:
$$2x - 7(5x + 26) = 16$$
Expand and simplify:
$$2x - 35x - 182 = 16$$
$$-33x = 16 + 182$$
$$-33x = 198$$
$$x = \frac{198}{-33} = -6$$

Step3: Solve for y using x=-6

Substitute $x=-6$ into $y = 5x + 26$:
$$y = 5(-6) + 26 = -30 + 26 = -4$$

Step4: Verify the solution

Check $(-6,-4)$ in both equations:

1. $-5(-6) + (-4) = 30 - 4 = 26$ (matches)
2. $2(-6) -7(-4) = -12 +28 =16$ (matches)

Answer:

d) (-6,-4)