Solve the system of equations by elimination.%0D%0A%0D%0A3x + 4y = 31%0D%0A2x – 4y = –6%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(4, 5)%0D%0A(4, 5)%0D%0A%0D%0A(5, 4)%0D%0A(5, 4)%0D%0A%0D%0A(–5, 12.5)%0D%0A(–5, 12.5)%0D%0A%0D%0A(5, –4)

Answer 1

To solve the system of equations by elimination, we'll add the two equations together to eliminate the variable "y":

(3x + 4y) + (2x - 4y) = 31 + (-6)

Combining like terms:

5x = 25

Divide both sides by 5 to solve for x:

x = 5

Now substitute the value of x back into either of the original equations, let's use the first equation:

3(5) + 4y = 31

15 + 4y = 31

Subtract 15 from both sides:

4y = 16

Divide both sides by 4 to solve for y:

y = 4

So the solution to the system of equations is (x, y) = (5, 4).

Therefore, the correct response is:

(5, 4)