Question

Solve the system of linear equations by multiplying.
{−2x + 2y =4
{−4x + 8y =24

Answer 1

The solution set is (2,4).

Explanation:

Given that:

−2x + 2y =4 Eqn 1

−4x + 8y =24 Eqn 2

Multiplying Eqn 1 by -2

-2(-2x+2y=4)

4x-4y= -8 Eqn 3

Adding Eqn 2 and 3

(-4x+8y)+(4x-4y)=24-8

-4x+8y+4x-4y=16

4y=16

Dividing both sides by 4

`(4y)/(4)=(16)/(4)\\y=4`

Putting y=4 in Eqn 1

-2x+2(4)=4

-2x+8=4

-2x=4-8

-2x=-4

Dividing both sides by -2

`(-2x)/(-2)=(-4)/(-2)\\x=2`

Hence,

The solution set is (2,4).