Solve by Substitution 3x=y -5x-10y=-35

$3 x = y$ $- 5 x - 10 y = - 35$

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

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

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

$- 5 x - 10 y = - 35$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$- 5 x - 10 y = - 35$

Divide $x$ by $1$ .

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

$- 5 x - 10 y = - 35$

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

$- 5 x - 10 y = - 35$

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

$- 5 x - 10 y = - 35$

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

$- 5 x - 10 y = - 35$

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

Replace all occurrences of $x$ in $- 5 x - 10 y = - 35$ with $\frac{y}{3}$ .

$- 5 \frac{y}{3} - 10 y = - 35$

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

Simplify the left side.

Simplify $- 5 \frac{y}{3} - 10 y$ .

Simplify each term.

Combine $- 5$ and $\frac{y}{3}$ .

$\frac{- 5 y}{3} - 10 y = - 35$

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

Move the negative in front of the fraction.

$- \frac{5 y}{3} - 10 y = - 35$

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

$- \frac{5 y}{3} - 10 y = - 35$

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

To write $- 10 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5 y}{3} - 10 y \cdot \frac{3}{3} = - 35$

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

Simplify terms.

Combine $- 10 y$ and $\frac{3}{3}$ .

$- \frac{5 y}{3} + \frac{- 10 y \cdot 3}{3} = - 35$

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

Combine the numerators over the common denominator.

$\frac{- 5 y - 10 y \cdot 3}{3} = - 35$

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

$\frac{- 5 y - 10 y \cdot 3}{3} = - 35$

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

Simplify the numerator.

Factor $5 y$ out of $- 5 y - 10 y \cdot 3$ .

Factor $5 y$ out of $- 5 y$ .

$\frac{5 y (- 1) - 10 y \cdot 3}{3} = - 35$

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

Factor $5 y$ out of $- 10 y \cdot 3$ .

$\frac{5 y (- 1) + 5 y (- 2 \cdot 3)}{3} = - 35$

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

Factor $5 y$ out of $5 y (- 1) + 5 y (- 2 \cdot 3)$ .

$\frac{5 y (- 1 - 2 \cdot 3)}{3} = - 35$

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

$\frac{5 y (- 1 - 2 \cdot 3)}{3} = - 35$

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

Multiply $- 2$ by $3$ .

$\frac{5 y (- 1 - 6)}{3} = - 35$

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

Subtract $6$ from $- 1$ .

$\frac{5 y \cdot - 7}{3} = - 35$

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

Multiply $- 7$ by $5$ .

$\frac{- 35 y}{3} = - 35$

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

$\frac{- 35 y}{3} = - 35$

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

Move the negative in front of the fraction.

$- \frac{35 y}{3} = - 35$

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

$- \frac{35 y}{3} = - 35$

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

$- \frac{35 y}{3} = - 35$

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

$- \frac{35 y}{3} = - 35$

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

Solve for $y$ in $- \frac{35 y}{3} = - 35$ .

Multiply both sides of the equation by $- \frac{3}{35}$ .

$- \frac{3}{35} \cdot (- \frac{35 y}{3}) = - \frac{3}{35} \cdot - 35$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{35} (- \frac{35 y}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{35}$ into the numerator.

$\frac{- 3}{35} \cdot (- \frac{35 y}{3}) = - \frac{3}{35} \cdot - 35$

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

Move the leading negative in $- \frac{35 y}{3}$ into the numerator.

$\frac{- 3}{35} \cdot \frac{- 35 y}{3} = - \frac{3}{35} \cdot - 35$

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

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{35} \cdot \frac{- 35 y}{3} = - \frac{3}{35} \cdot - 35$

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

Cancel the common factor.

$\frac{3 \cdot - 1}{35} \cdot \frac{- 35 y}{3} = - \frac{3}{35} \cdot - 35$

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

Rewrite the expression.

$\frac{- 1}{35} \cdot (- 35 y) = - \frac{3}{35} \cdot - 35$

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

$\frac{- 1}{35} \cdot (- 35 y) = - \frac{3}{35} \cdot - 35$

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

Cancel the common factor of $35$ .

Factor $35$ out of $- 35 y$ .

$\frac{- 1}{35} \cdot (35 (- y)) = - \frac{3}{35} \cdot - 35$

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

Cancel the common factor.

$\frac{- 1}{35} \cdot (35 (- y)) = - \frac{3}{35} \cdot - 35$

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

Rewrite the expression.

$y = - \frac{3}{35} \cdot - 35$

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

$y = - \frac{3}{35} \cdot - 35$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{35} \cdot - 35$

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

Multiply $y$ by $1$ .

$y = - \frac{3}{35} \cdot - 35$

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

$y = - \frac{3}{35} \cdot - 35$

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

$y = - \frac{3}{35} \cdot - 35$

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

$y = - \frac{3}{35} \cdot - 35$

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

Simplify the right side.

Simplify $- \frac{3}{35} \cdot - 35$ .

Cancel the common factor of $35$ .

Move the leading negative in $- \frac{3}{35}$ into the numerator.

$y = \frac{- 3}{35} \cdot - 35$

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

Factor $35$ out of $- 35$ .

$y = \frac{- 3}{35} \cdot (35 (- 1))$

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

Cancel the common factor.

$y = \frac{- 3}{35} \cdot (35 \cdot - 1)$

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

Rewrite the expression.

$y = - 3 \cdot - 1$

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

$y = - 3 \cdot - 1$

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

Multiply $- 3$ by $- 1$ .

$y = 3$

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

$y = 3$

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

$y = 3$

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

$y = 3$

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

$y = 3$

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

Replace all occurrences of $y$ with $3$ in each equation.

Replace all occurrences of $y$ in $x = \frac{y}{3}$ with $3$ .

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

$y = 3$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, 3)$

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Solve by Substitution 3x=y -5x-10y=-35

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