Solve by Substitution 3x-30=y 7y-6=3x

$3 x - 30 = y$ $7 y - 6 = 3 x$

Rewrite the equation as $y = 3 x - 30$ .

$y = 3 x - 30$

$7 y - 6 = 3 x$

Replace all occurrences of $y$ with $3 x - 30$ in each equation.

Replace all occurrences of $y$ in $7 y - 6 = 3 x$ with $3 x - 30$ .

$7 (3 x - 30) - 6 = 3 x$

$y = 3 x - 30$

Simplify the left side.

Simplify $7 (3 x - 30) - 6$ .

Simplify each term.

Apply the distributive property.

$7 (3 x) + 7 \cdot - 30 - 6 = 3 x$

$y = 3 x - 30$

Multiply $3$ by $7$ .

$21 x + 7 \cdot - 30 - 6 = 3 x$

$y = 3 x - 30$

Multiply $7$ by $- 30$ .

$21 x - 210 - 6 = 3 x$

$y = 3 x - 30$

$21 x - 210 - 6 = 3 x$

$y = 3 x - 30$

Subtract $6$ from $- 210$ .

$21 x - 216 = 3 x$

$y = 3 x - 30$

$21 x - 216 = 3 x$

$y = 3 x - 30$

$21 x - 216 = 3 x$

$y = 3 x - 30$

$21 x - 216 = 3 x$

$y = 3 x - 30$

Solve for $x$ in $21 x - 216 = 3 x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$21 x - 216 - 3 x = 0$

$y = 3 x - 30$

Subtract $3 x$ from $21 x$ .

$18 x - 216 = 0$

$y = 3 x - 30$

$18 x - 216 = 0$

$y = 3 x - 30$

Add $216$ to both sides of the equation.

$18 x = 216$

$y = 3 x - 30$

Divide each term in $18 x = 216$ by $18$ and simplify.

Divide each term in $18 x = 216$ by $18$ .

$\frac{18 x}{18} = \frac{216}{18}$

$y = 3 x - 30$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{216}{18}$

$y = 3 x - 30$

Divide $x$ by $1$ .

$x = \frac{216}{18}$

$y = 3 x - 30$

$x = \frac{216}{18}$

$y = 3 x - 30$

$x = \frac{216}{18}$

$y = 3 x - 30$

Simplify the right side.

Divide $216$ by $18$ .

$x = 12$

$y = 3 x - 30$

$x = 12$

$y = 3 x - 30$

$x = 12$

$y = 3 x - 30$

$x = 12$

$y = 3 x - 30$

Replace all occurrences of $x$ with $12$ in each equation.

Replace all occurrences of $x$ in $y = 3 x - 30$ with $12$ .

$y = 3 (12) - 30$

$x = 12$

Simplify the right side.

Simplify $3 (12) - 30$ .

Multiply $3$ by $12$ .

$y = 36 - 30$

$x = 12$

Subtract $30$ from $36$ .

$y = 6$

$x = 12$

$y = 6$

$x = 12$

$y = 6$

$x = 12$

$y = 6$

$x = 12$

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

$(12, 6)$

The result can be shown in multiple forms.

Point Form:

$(12, 6)$

Equation Form:

$x = 12, y = 6$

Solve by Substitution 3x-30=y 7y-6=3x

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