MATH SOLVE

4 months ago

Q:
# Need help AsapA: 10x β 4y = 20B: 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

Accepted Solution

A:

x = 44/23 and y= -5/23.

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)Β β 30x-12y=60

2(8x+6y=14)Β βΒ 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+28Β

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 = 20/23Β Γ· -4/1

y = 20/23Β Γ -1/4 = -20/92 = -5/23

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)Β β 30x-12y=60

2(8x+6y=14)Β βΒ 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+28Β

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 = 20/23Β Γ· -4/1

y = 20/23Β Γ -1/4 = -20/92 = -5/23