Question

Solve the simultaneous equations
4x+3y=11
2x-y=-2

Answer 1

`x = (1)/(2)`

`y = 3`

Explanation:

Multiply the bottom equation by -2.

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

Add the new equation to top equation.

`5y = 15`

`y = 3`

Know plug 3 in one of the equations to find x.

`4x + 3(3) = 11`

`4x = 2`

`x = (1)/(2)`

Answer 2

(
`(1)/(2)`, 3 )

Explanation:

Given the 2 equations

4x + 3y = 11 → (1)

2x - y = - 2 → (2)

Multiplying (2) by 3 and adding to (1) will eliminate the y- term

6x - 3y = - 6 → (3)

Add (1) and (3) term by term to eliminate y

10x + 0 = 5

10x = 5 ( divide both sides by 10 )

x =
`(1)/(2)`

Substitute x =
`(1)/(2)` into either of the 2 equations and solve for y

Substituting into (1)

4 (
`(1)/(2)` ) + 3y = 11

2 + 3y = 11 ( subtract 2 from both sides )

3y = 9 ( divide both sides by 3 )

y = 3

solution is (
`(1)/(2)`, 3 )