Question

Elimination 5x -6y = -17. -3x -5y = -7

Answer 1

x = -1

y = 2

Explanation:

5x - 6y = -17

-3x - 5y = -7

I will eliminate variable x first:

Multiply the first equation by 3

15x - 18y = -51

Multiply the second equation by 5

-15x - 25y = -35

Now subtract the second equation from the first equation:

15x - 18y = -51

-15x - 25y = -35

0x - 43y = -86

-43y = -86

Divide both sides by -43

Negative + Negative = Positive

y = 2

Now eliminate variable y:

Multiply the first equation by 5

25x - 30y = -85

Multiply the second equation by -6 (Negative switches all of the signs)

18x + 30y = 42

43x + 0y = -43

43x = -43

Divide both sides by 43

x = -1

Check work:

5(-1) - 6(2) = -17

-5 - 12 = -17

-17 = -17

Correct

-3(-1) - 5(2) = -7

3 - 10 = -7

-7 = -7

Correct

Answer 2

x = -1 and y = 2

Explanation:

3(5x - 6y = -17)

5(-3x - 5y = -7)

----------------------- Add the two equations together

-43y = -86

y = 2

5x - 6(2) = -17 Substitute y with 2 in the first equation to get the value of x

x = -1