# 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

Question

Answer:

x=44/23, y=-5/23We 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)

solved

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