Solve the system of equations and choose the correct ordered pair.

5x + 7y = 13
12x - 5y = -56

Question

Solve the system of equations and choose the correct ordered pair.

5x + 7y = 13
12x - 5y = -56

anonymous · Answer

$$x=-3,y=4$$

anonymous · Answer

use elimination, multiply every element in the top equation by 5 and every element in the bottom equation by 7

25x+35y=65
84x-35y=-392


Notice how the coeefficients in front of the y are equal but opposite, add the two equations thus eliminating the y in the process:

109x +0y=-327

anonymous · Answer

no solve for x, where x=-327/109 = -3

anonymous · Answer

knowing the value for x you can substitute it into any of the two equations, choose the easiest one (the one with smaller numbers) 5(-3)+7y=13

anonymous · Answer

7y=13+15=28
y=28/7=4

anonymous · Answer

I reached the same conclusion using substitution (which maybe takes longer in this particular problem) instead of the ordered pair approach. My work is in the attached file.