Question

Solve the simultaneous equations
4x + 5y = 9
4x - 2y = 2

Answer 1

x = 1 and y = 1

Explanation:

Let's solve your system by substitution.

4x + 5y = 9 ; 4x − 2y = 2

- Solve 4x + 5y = 9 for x:

4x + 5y = 9

4x + 5y + − 5y = 9 + − 5y (Add -5y to both sides)

4x = − 5y + 9

`(4)/(x) = (- 5y + 9)/(4)`

`x = (- 5)/(4) y + (9)/(4)`

Then Substitute
`(- 5)/(4) y + (9)/(4)` for x in 4x - 2y = 2

4x − 2y = 2

4(
`(- 5)/(4) y + (9)/(4)`) − 2y = 2

− 7y + 9 = 2 (Simplify both sides of the equation)

− 7y + 9 + − 9 = 2 + − 9 (Add -9 to both sides)

− 7y = − 7

`(- 7y)/(- 7) = (- 7)/(- 7)` (Divide both sides by -7)

y = 1

Substitute 1 for y in x =
`(- 5)/(4) y + (9)/(4)`

`x = (- 5)/(4) y + (9)/(4)`

`x = (- 5)/(4) (1) + (9)/(4)`

x = 1

So, x = 1 and y = 1