Question

Y = 2/3 x + 1 y = 4/3x - 1

Answer 1

We will use graphical method to solve for x and y

• y=2/3x+1
• y=4/3x-1

Graph attached

The solution is

• (3,3)

Answer 2

x = 3

Explanation:

Given system of equations:

`\begin{cases}y=(2)/(3)x+1\\\\y =(4)/(3)x-1\end{cases}`

To solve, use the substitution method:

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

Add 1 to both sides:

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

`\implies (2)/(3)x+2=(4)/(3)x`

Subtract 2/3 x from both sides:

`\implies (2)/(3)x+2-(2)/(3)x=(4)/(3)x-(2)/(3)x`

`\implies 2=(2)/(3)x`

Multiply both sides by 3:

`\implies 3 \cdot2=3 \cdot (2)/(3)x`

`\implies 6=2x`

Divide both sides by 2:

`\implies (6)/(2)=(2x)/(2)`

`\implies 3=x`

Therefore:

`\implies x=3`