Question

-5x + 4y = -22
-3x – 4y = -26

Answer 1

x = 6

y = 2

Explanation:

Solve for x in the first equation:

-5x + 4y = -22

Step 1 - Subtract 4y from both sides:

-5x + 4y - 4y = -22 - 4y

-5x = -22 - 4y

Step 2 - Change every operation to its opposite counterpart:

5x = 22 + 4y

Divide both sides by 5:

`(5x)/(5) =( (22 + 4y) )/(5)`

`x = ( (22 + 4y) )/(5)`

Step 3 - Now substitute this into the second equation:

-3x - 4y = -26

-3(
`( (22 + 4y) )/(5)`) - 4y = -26

-3(
`(1)/(5)(22+4y)`)

`(-3)/(1) * (1)/(5) = (-3)/(5)`

`(-3)/(5)(22 + 4y) - 4y = -26`

Step 4 - Multiply both sides by 5:

`-3(22 + 4y) - 5(4y) = -(5)26\\-3(22 + 4y) - 20y = -130`

Step 5 - Simplify the brackets

`-66 -12y - 20y = -130`

130 = 66 + 12y + 20y

130 = 66 + 32y

Step 6 - Subtract 66 from both sides of the equation;

130 - 66 = 66 + 32y - 66

64 = 32y

Step 7 - Divide both sides by 32:

`(64)/(32) = (32y)/(32)`

2 = y

Step 8 - So y = 2, so now we can substitute this into one of the equations:

-5x + 4y = -22

-5x + 4(2) = -22

-5x + 8 = -22

Subtract 8 from both sides

-5x + 8 - 8 = -22 - 8

-5x = -30

5x = 30

Divide both sides by 5:

`(5x)/(5) = (30)/(5)`

x = 6

Hope this helps!