We want the coefficient of one of the variables to be the same in both equations; we can multiply the top equation by 3 and the bottom equation by 2 to make the coefficients of y equal: 3(10x-4y=20) → 30x-12y=60 2(8x+6y=14) → 16x+12y=28
This is possible due to the multiplication property of equality.
Now that the coefficients of y are the same, we can add the equations together (using the addition property of equality): 30x+16x = 60+28 46x = 88 (addition of like terms)
Divide both sides by 46: 46x/46 = 88/46 (division property of equality) x = 88/46 = 44/23
Now we substitute x into the first equation: 10(44/23) - 4y = 20 440/23 - 4y = 20
It will be easier to solve this if we have a common denominator; 20 wholes = (20*23)/23 = 460/23;
440/23 - 4y = 460/23
Subtract 440/23 from both sides (subtraction property of equality): 440/23 - 4y - 440/23 = 460/23 - 440/23 -4y = 20/23
Divide both sides by -4 (division property of equality): -4y/-4 = 20/23 ÷ -4/1 y = 20/23 × -1/4 = -20/92 = -5/23
