Question

Solve the system of equations minus, 2, x, plus, 2, y, equals, 8−2x+2y=8 and 4, x, minus, 7, y, equals, minus, 434x−7y=−43 by combining the equations.
Below, two sets of the two equations are shown. The first set has input boxes in front of each equation to put a number to multiply it by. When you enter a number, the corresponding equation below changes to be the result of the multiplication. Under the second set, a resulting equation is shown with input boxes for the coefficients and constant. Then, there is a "try" button. When you press the try button, if your answer is correct, it will be placed on the page and a new question will appear with a new input box. This process will continue until the final answer area appears with the submit button.
left parenthesis, minus, 2, x(−2x plus, 2, y+2y equals= 8, right parenthesis8)
left parenthesis, 4, x(4x minus, 7, y−7y equals= minus, 43, right parenthesis−43)
minus, 2, x−2x plus, 2, y+2y equals= 88
4, x4x minus, 7, y−7y equals= minus, 43−43
0
0xx plus+
0
0yy equals=

Answer 1

Use elimination. Multiply the first equation by 2 to get
-4x + 4y = 16.
Add this to the second equation 4x − 7y = −43:
(-4x+4y) + (4x−7y) = 16 + (−43) → −3y = −27 → y = 9.

Substitute y = 9 into −2x + 2y = 8:
−2x + 2(9) = 8 → −2x + 18 = 8 → −2x = −10 → x = 5.

Solution: (x, y) = (5, 9).