Solve by Addition/Elimination 3x+2y=2 and -3x+5y=5

$3 x + 2 y = 2$ and $- 3 x + 5 y = 5$

Add the two equations together to eliminate $x$ from the system.

Divide each term in $7 y = 7$ by $7$ and simplify.

Divide each term in $7 y = 7$ by $7$ .

$\frac{7 y}{7} = \frac{7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{7}{7}$

Divide $y$ by $1$ .

$y = \frac{7}{7}$

Simplify the right side.

Divide $7$ by $7$ .

$y = 1$

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$3 x + 2 (1) = 2$

Multiply $2$ by $1$ .

$3 x + 2 = 2$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$3 x = 2 - 2$

Subtract $2$ from $2$ .

$3 x = 0$

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

The solution to the independent system of equations can be represented as a point.

$(0, 1)$

The result can be shown in multiple forms.

Point Form:

$(0, 1)$

Equation Form:

$x = 0, y = 1$