Question

`3x+5y=7\\9x+11y=13` Solve for the variables.

Answer 1

-1, 2

Explanation:

Although you already have the answer, here's another method of doing it that may or may not help you someday. First, we solve the top equation for x. We get:

`x = (7)/(3) - (5)/(3)y\\9x + 11y = 13`

Now that we know what x is, we can plug it into the bottom equation to solve for y.

`9((7)/(3) - (5)/(3)y) + 11y = 13`

Simplify everything out, and you'll see that y = 2. We can now plug it into our equation to solve for x.

x = 7/3 - 5/3 x 2; x = -1

Answer 2

x = -1

y =2

Explanation:

3x+ 5y = 7

9x+ 11y = 13

Multiply the first equation by -3 so we can eliminate x

-3 (3x+ 5y = 7)

-9x -15y = -21

Add this to the second equation

-9x -15y = -21

9x+ 11y = 13

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

- 4y = -8

Divide by -4

-4y/-4 = -8/-4

y=2

Now solve for x

3x+5y = 7

3x+5(2) = 7

3x+10 = 7

Subtract 10

3x = 7-10

3x = -3

Divide by 3

3x/3 = -3/3

x = -1