Question

A: 10x − 4y = 20 B: 8x + 6y = 14 Solve this system of equations using addition. Show all of your work. Also list the property that you use in each step

Answer 1

X=44/23, y=-5/23

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)