Question

Solve the linear system of equations using the linear combination method. {8a−4b=205a−8b=62

Answer 1

Step 1:

Line up respective variables in column.

$8a-4b=20$.................(1)

$5a-8b=62$.................................(2)

Step 2:

We need to multiply first equation with -2 so that the coefficient of b becomes equal and opposite of -8.

$8a-4b=20$ *2

$-16a + 8b=-40$ ...................(3)

Step 3:

Add equation (2) and (3)

$5a-8b=62$

$-16a+8b=-40$

The b terms will cancel out and we are left with only a terms.

-11a = 22

dividing both sides by -11

a=-2

Step 4:

plug this value of a in equation (1) to find value of b,

$8a-4b=20$

$8(-2)-4b=20$

$-16-4b=20$

b=-9

Answer : a=-2 and b =-9