Question

Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16?

(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)

Answer 1

(–6, –4)

Explanation:

After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)

Answer 2

(–6, –4)

Explanation:

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.

It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.

Using the substitution method, make y the subject in the first equation

y = 5x + 26

substitute into the second equation

2x -7(5x + 26) = 16

-33x - 182 = 16

-33x = 16 + 182

-33x = 198

x = 198/-33

x = -6

since y = 5x + 26

y = 5(-6) + 26

= -30 + 26

= -4

hence (x,y) = (-6,-4)