Question

What is the value of the x variable in the solution to the following system of equations? 4x − 3y = 3 5x − 4y = 3

Answer 1

Solve 4x − 3y = 3 and 5x − 4y = 3

Step 1: Solve for x in 4x-3y=3:
4x-3y=3
4x-3y+3y=3+3y [Add 3y to both sides]
4x=3y+3

`(4x)/(4) = (3x+3)/(4)` [Divide both sides by 4]
x=
`(3)/(4)y+ (3)/(4)`

Step 2: Substitute
`(3)/(4)y+ (3)/(4)` for x in 5x-4y=3
5x-4y=3
5(
`(3)/(4)y+ (3)/(4)`)-4y=3

`(-1)/(4)y+ (15)/(4) =3`

`(-1)/(4)y+ (15)/(4) - (15)/(4) =3- (15)/(4)` [Subtract
`(15)/(4)` to both sides]

`(-1)/(4)y= (-3)/(4)`

`( (-1)/(4)y)/( (-1)/(4) )= ((-3)/(4) )/( (-1)/(4))` [Divide both sides by
`(-1)/(4)` ]
y = 3

Step 3: Substitute 3 for y in x =
`(3)/(4)y+ (3)/(4)`

`(3)/(4)y+ (3)/(4)`

`(3)/(4)(3)+ (3)/(4)`
x = 3