We first want to make the coefficients of one of the variables the same. If we choose y, we can do this by multiplying the first equation by 3 and the second equation by 2:
3(10x-4y=20)→30x-12y=60 2(8x+6y=14)→16x+12y=28
This is due to the multiplication property of equality.
Next we add the two equations together: 30x-12y=60 +(16x+12y=28) → 46x = 88
This is due to addition.
Next we divide both sides by 46: 46x/46 = 88/46 x = 88/46 = 44/23
This is due to the division property of equality.
Next we substitute this into the first equation: 10(44/23)-4y=20 440/23 - 4y = 20
This is due to multiplication.
We want a common denominator in order to cancel the 440/23; 23 wholes = 460/23:
440/23 - 4y = 460/23 (substitution)
Subtract 440/23 from both sides: 440/23 - 4y - 440/23 = 460/23 - 440/23 -4y = 20/23
This is the subtraction property of equality.
Next, divide both sides by -4: -4y/-4 = 20/23 ÷ -4 y = 20/23 ÷ -4/1 y = 20/23 × -1/4 = -20/92 = -10/46 = -5/23 (division property of equality)
