Question

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

Answer 1

Answer:

x = 3

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=\dfrac{2}{3}x+1\\\\y =\dfrac{4}{3}x-1\end{cases}$

To solve, use the substitution method:

$\implies \dfrac{2}{3}x+1=\dfrac{4}{3}x-1$

Add 1 to both sides:

$\implies \dfrac{2}{3}x+1+1=\dfrac{4}{3}x-1+1$

$\implies \dfrac{2}{3}x+2=\dfrac{4}{3}x$

Subtract 2/3 x from both sides:

$\implies \dfrac{2}{3}x+2-\dfrac{2}{3}x=\dfrac{4}{3}x-\dfrac{2}{3}x$

$\implies 2=\dfrac{2}{3}x$

Multiply both sides by 3:

$\implies 3 \cdot2=3 \cdot \dfrac{2}{3}x$

$\implies 6=2x$

Divide both sides by 2:

$\implies \dfrac{6}{2}=\dfrac{2x}{2}$

$\implies 3=x$

Therefore:

$\implies x=3$

Answer 2

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)