Question

Y = 7

x + y = 6

What is the solution of the system shown?

(, 14)
(6, 12)
(10 , 5)

Answer 1

10 2/3, 5)

Explanation:

1/2 x + 1/3y = 7

1/4x + 2/3y = 6

I do not like fractions so I will multiply the first equation by 6 and the second equation by 12 to eliminate the fractions.

6(1/2 x + 1/3y) = 7*6

Distribute

3x+2y = 42

Now the second

12(1/4x + 2/3y) = 6*12

3x+8y = 72

My system of equation is

3x+2y = 42

3x+8y = 72

Subtracting the second from the first

3x+2y = 42

-3x-8y = -72

-------------------

-6y = -30

Divide by -6

-6y/-6 = -30/-6

y =5

Substituting into 3x+2y = 42

3x+2(5) = 42

3x+10 =42

Subtracting 10 from each side

3x+10-10 =42-10

3x= 32

Dividing by 3

3x/3 = 32/3

x = 32/3 or 10 2/3

Answer 2

(10 2/3, 5)

Explanation:

1/2 x + 1/3y = 7

1/4x + 2/3y = 6

I do not like fractions so I will multiply the first equation by 6 and the second equation by 12 to eliminate the fractions.

6(1/2 x + 1/3y) = 7*6

Distribute

3x+2y = 42

Now the second

12(1/4x + 2/3y) = 6*12

3x+8y = 72

My system of equation is

3x+2y = 42

3x+8y = 72

Subtracting the second from the first

3x+2y = 42

-3x-8y = -72

-------------------

-6y = -30

Divide by -6

-6y/-6 = -30/-6

y =5

Substituting into 3x+2y = 42

3x+2(5) = 42

3x+10 =42

Subtracting 10 from each side

3x+10-10 =42-10

3x= 32

Dividing by 3

3x/3 = 32/3

x = 32/3 or 10 2/3