Question

Solve the following system using ANY method.

8a - 4b = 20 5a - 8b = 62

Question 5 options:

a = 5, b = -4


a = 8, b = 4


a = -5, b = -8


a = -2, b = -9

Answer 1

a=-2 and b=-9

Explanation:

To solve the system, substitute one equation into another.

8a -4b = 20 becomes -4b = 20 - 8a. Dividing by -4 on both sides, b = 2a-5.

Now substitute the equation b=2a-5 into 5a - 8b = 62.

5a - 8(2a-5) = 62

5a - 16a + 40 = 62

-11a + 40 = 62

-11a = 22

a=-2

To find b, substitute a=-2 into b=2a-5.

b = 2(-2) - 5

b = -4 - 5

b = -9