Question

Solve the following system using substitution.

Answer 1

Answer/Step-by-step explanation:

3. By substitution method, let's substitute
`(2)/(3)x- 4` for y in the first equation.

Thus,

`(1)/(3)x + 2((2)/(3)x- 4) = 1`

Solve for x

`(x)/(3) + (4x)/(3) - 4 = 1`

Add 4 to both sides

`(x)/(3) + (4x)/(3) - 4 + 4 = 1 + 4`

`(x)/(3) + (4x)/(3) = 5`

`(x + 4x)/(3) = 5`

`(5x)/(3) = 5`

Multiply both sides by 3

`(5x)/(3)*3 = 5*3`

`5x = 15`

Divide both sides by 5

`x = 3`

Now, substitute 3 for x in the equation.

`y = (2)/(3)x- 4`

`y = (2)/(3)(3) - 4`

`y = 2 - 4`

`y = -2`

The solution of the equation is x = 3, y = -2

4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.

`3x - 2y = 11`

`-3x - y = 4`

`-3y = 15` =>
`(-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15)`

Divide both sides by -3 to solve for y

`(-3y)/(-3) = (15)/(-3)`

`y = -5`

Substitute -5 for y in the first equation to find x

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

`3x + 10 = 11`

Subtract 10 from both sides

`3x + 10 - 10 = 11 - 10`

`3x = 1`

Divide both sides by 3

`(3x)/(3) = (1)/(3)`

`x = (1)/(3)`

The solution is
`x = (1)/(3), y = -5`