Question

Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.

Answer 1

See explanation for matching pairs

Explanation:

Equations

(1)

`x - y = 25`

`2x + 3y = 180`

(2)

`2x - 3y = -5`

`11x + y = 550`

(3)

`x - y = 19`

`-12x + y = 168`

Solutions

`(-17,-36)`

`(47, 33)`

`(51, 26)`

Required

Match equations with solutions

(1)
`x - y = 25` and
`2x + 3y = 180`

Make x the subject in:
`x - y = 25`

`x = 25 + y`

Substitute
`x = 25 + y` in
`2x + 3y = 180`

`2(25 + y) + 3y = 180`

`50 + 2y + 3y = 180`

`50 + 5y = 180`

Collect like terms

`5y = 180-50`

`5y = 130`

Solve for y

`y =26`

Recall that:
`x = 25 + y`

`x = 25 + 26`

`x = 51`

So:

`(x,y) = (51,26)`

(2)
`2x - 3y = -5` and
`11x + y = 550`

Make y the subject in
`11x + y = 550`

`y = 550 - 11x`

Substitute
`y = 550 - 11x` in
`2x - 3y = -5`

`2x - 3(550 - 11x) = -5`

`2x - 1650 + 33x = -5`

Collect like terms

`2x + 33x = -5+1650`

`35x = 1645`

Solve for x

`x = 47`

Solve for y in
`y = 550 - 11x`

`y = 550 - 11 * 47`

`y = 550 - 517`

`y = 33`

So:

`(x,y) = (47,33)`

(3)

`x - y = 19` and
`-12x + y = 168`

Make y the subject in
`-12x + y = 168`

`y = 168 + 12x`

Substitute
`y = 168 + 12x` in
`x - y = 19`

`x - 168 - 12x = 19`

Collect like terms

`x -12x = 168 + 19`

`-11x = 187`

Solve for x

`x = -17`

Solve for y in
`y = 168 + 12x`

`y =168-12 *17`

`y =-36`

So:

`(x,y) = (-17,-36)`