Solve the System of Equations 3x+5y=9 30x+50y=-90

$3 x + 5 y = 9$ $30 x + 50 y = - 90$

Solve for $x$ in $3 x + 5 y = 9$ .

Subtract $5 y$ from both sides of the equation.

$3 x = 9 - 5 y$

$30 x + 50 y = - 90$

Divide each term in $3 x = 9 - 5 y$ by $3$ and simplify.

Divide each term in $3 x = 9 - 5 y$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3} + \frac{- 5 y}{3}$

$30 x + 50 y = - 90$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3} + \frac{- 5 y}{3}$

$30 x + 50 y = - 90$

Divide $x$ by $1$ .

$x = \frac{9}{3} + \frac{- 5 y}{3}$

$30 x + 50 y = - 90$

$x = \frac{9}{3} + \frac{- 5 y}{3}$

$30 x + 50 y = - 90$

$x = \frac{9}{3} + \frac{- 5 y}{3}$

$30 x + 50 y = - 90$

Simplify the right side.

Simplify each term.

Divide $9$ by $3$ .

$x = 3 + \frac{- 5 y}{3}$

$30 x + 50 y = - 90$

Move the negative in front of the fraction.

$x = 3 - \frac{5 y}{3}$

$30 x + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

$30 x + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

$30 x + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

$30 x + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

$30 x + 50 y = - 90$

Replace all occurrences of $x$ with $3 - \frac{5 y}{3}$ in each equation.

Replace all occurrences of $x$ in $30 x + 50 y = - 90$ with $3 - \frac{5 y}{3}$ .

$30 (3 - \frac{5 y}{3}) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Simplify the left side.

Simplify $30 (3 - \frac{5 y}{3}) + 50 y$ .

Simplify each term.

Apply the distributive property.

$30 \cdot 3 + 30 (- \frac{5 y}{3}) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Multiply $30$ by $3$ .

$90 + 30 (- \frac{5 y}{3}) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5 y}{3}$ into the numerator.

$90 + 30 (\frac{- 5 y}{3}) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Factor $3$ out of $30$ .

$90 + 3 (10) (\frac{- 5 y}{3}) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Cancel the common factor.

$90 + 3 \cdot (10 (\frac{- 5 y}{3})) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Rewrite the expression.

$90 + 10 (- 5 y) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

$90 + 10 (- 5 y) + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Multiply $- 5$ by $10$ .

$90 - 50 y + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

$90 - 50 y + 50 y = - 90$

$x = 3 - \frac{5 y}{3}$

Combine the opposite terms in $90 - 50 y + 50 y$ .

Add $- 50 y$ and $50 y$ .

$90 + 0 = - 90$

$x = 3 - \frac{5 y}{3}$

Add $90$ and $0$ .

$90 = - 90$

$x = 3 - \frac{5 y}{3}$

$90 = - 90$

$x = 3 - \frac{5 y}{3}$

$90 = - 90$

$x = 3 - \frac{5 y}{3}$

$90 = - 90$

$x = 3 - \frac{5 y}{3}$

$90 = - 90$

$x = 3 - \frac{5 y}{3}$

Since $90 = - 90$ is not true, there is no solution.

No solution

Solve the System of Equations 3x+5y=9 30x+50y=-90

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