Solve the System of Equations 3x+2y=2 and y=-1.5x+1

$3 x + 2 y = 2$ and $y = - 1.5 x + 1$

Replace all occurrences of $y$ with $- 1.5 x + 1$ in each equation.

Replace all occurrences of $y$ in $3 x + 2 y = 2$ with $- 1.5 x + 1$ .

$3 x + 2 (- 1.5 x + 1) = 2$

$y = - 1.5 x + 1$

Simplify the left side.

Simplify $3 x + 2 (- 1.5 x + 1)$ .

Simplify each term.

Apply the distributive property.

$3 x + 2 (- 1.5 x) + 2 \cdot 1 = 2$

$y = - 1.5 x + 1$

Multiply $- 1.5$ by $2$ .

$3 x - 3 x + 2 \cdot 1 = 2$

$y = - 1.5 x + 1$

Multiply $2$ by $1$ .

$3 x - 3 x + 2 = 2$

$y = - 1.5 x + 1$

$3 x - 3 x + 2 = 2$

$y = - 1.5 x + 1$

Simplify by adding terms.

Subtract $3 x$ from $3 x$ .

$0 x + 2 = 2$

$y = - 1.5 x + 1$

Simplify the expression.

Multiply $0$ by $x$ .

$0 + 2 = 2$

$y = - 1.5 x + 1$

Add $0$ and $2$ .

$2 = 2$

$y = - 1.5 x + 1$

$2 = 2$

$y = - 1.5 x + 1$

$2 = 2$

$y = - 1.5 x + 1$

$2 = 2$

$y = - 1.5 x + 1$

$2 = 2$

$y = - 1.5 x + 1$

$2 = 2$

$y = - 1.5 x + 1$

Remove any equations from the system that are always true.

$y = - 1.5 x + 1$