Question

Use elimination to find the solution to the system of equations.

Answer 1

Answer:  option B.

Step-by-step explanation:

You can apply the elimination method:

- Multiply the first equation by -7 and the second equation by 3.

- Add both equations to cancel out the variable y.

- Solve for x

$\left \{ {{(-7)9x+3y=(-39)(-7)} \atop {(3)(4x+7y)=(-57)(3)}} \right.\\\\\left \{ {{-63x-21y=273} \atop {12x+21y=-171}} \right.\\-------\\-51x=102\\x=-2$

- Substitute x=-2 into any of the original equations ans solve for y. Then:

$9(-2)+3y=-39\\-18+3y=-39\\3y=-21\\y=-7$

Answer 2

Hello!

The answer is:

B.

$x=-2\\y=-7$

Why?

Solving the system of equations by elimination, we have:

$\left \{ {{9x+3y=-39} \atop {4x+7y=-57}} \right.$

Then, multiplying the second equation by $-\frac{9}{4}$

So,

$\left \{ {{9x+3y=-39} \atop {4x*(-\frac{9}{4}) +7y*(-\frac{9}{4}) =-57*(-\frac{9}{4})}} \right\\\\\left \{ {{9x+3y=-39} \atop {-9x-\frac{63}{4}y=\frac{513}{4} }} \right\\\\-\frac{51}{4}y=\frac{357}{4}\\\\y=\frac{357}{4}*(-\frac{4}{51})=-\frac{1428}{204}=-7$

Then, substituting y=-7 into the first equation (also, we could substitute it into the first equation) we have:

$9x+3(-7)=-39\\9x-21=-39\\9x=-39+21\\9x=-18\\x=\frac{-18}{9}=-2$

So, the solutions for the system of equations are:

$x=-2\\y=-7$

Have a nice day!