Question

13x=-21-6y and -8x=36+6y

Answer 1

x=3

y=-10

Explanation:

13x=-21-6y...............(1)

-8x=36+6y................(11)

Add (11) to (1)

5x=15-6y+6y

5x=15

Divide both sides by 5

5x/5=15/5

x=3

Substitute x=3 in 13x=-21-6y

13(3)=-21-6y

39=-21-6y

Collect like terms

39+21=-6y

60=-6y

Divide both sides by -6

60/-6=-6y/-6

-10=y

y=-10

Answer 2

`x=3\\y=-10`

Explanation:

`13x=-21-6y\\-8x=36+6y`

Let's take one of the equations and solve for x. I'll take the first one.

`13x=-21-6y`

Divide by 13.

`x=(-21-6y)/(13)`

Now replace x in the second equation.

`-8x=36+6y\\-8((-21-6y)/(13) )=36+6y`

Distribute -8

`(168+48y)/(13)=36+6y`

Break down the fraction.

`(168)/(13)+(48)/(13)y=36+6y`

Subtract
`(168)/(13)`

`(48)/(13)y=36+6y-(168)/(13)`

Subtract 6y

`(48)/(13)y-6y=36-(168)/(13)`

Combine like terms;

`(48-13*6)/(13)y=(36*13-168)/(13)`

Solve;

`(48-78)/(13)y=(468-168)/(13)`

Keep solving;

`(-30)/(13)y=(300)/(13)`

Multiply by the negative reciprocal of the fraction next to y.

`(-(13)/(30) )(-30)/(13)y=(300)/(13)(-(13)/(30) )`

On the right side; 13 and 13 become 1. 300/30 = 30/3 = 10

`y=-10`

After having found y, replace it in any of the equations to find x.

`13x=-21-6y\\13x=-21-6(-10)\\13x=-21+60\\13x=39\\x=(39)/(13)\\ x=3`