Question 2(Multiple Choice Worth 1 points) (06.01) Solve 2x + 5y = −13 3x − 4y = −8 (4, 1) (−4, 1) (4, −1) (−4, −1)

ANSWER

The solution is
[tex](-4,-1)[/tex]


EXPLANATION

The given equations are:

[tex]2x + 5y = - 13...(1)[/tex]

and

[tex]3x - 4y = - 8...(2)[/tex]


We multiply equation 1 by 3 to get,

[tex]6x + 15y = - 39...(3)[/tex]

We multiply equation 2 also by 2 to get,

[tex]6x - 8y = - 16...(4)[/tex]

We subtract equation 4 from equation 3 to get,


[tex]23y = - 23[/tex]
This implies that,

[tex]y = - 1[/tex]

We put this value of y into any of the equations say equation 2

[tex]3x - 4( - 1) = - 8[/tex]
Simplify

[tex]3x + 4 = - 8[/tex]
Group like terms
[tex]3x = - 8 - 4[/tex]
Simplify,

[tex]3x = - 12[/tex]

Divide both sides by 3 to get,

[tex]x = - 4[/tex]


Therefore the solution is
[tex](-4,-1)[/tex]

The correct answer is option D.