Solve by Substitution 3x+4y=19 , 3x+6y=33

$3 x + 4 y = 19$ , $3 x + 6 y = 33$

Step 1

Solve for $x$ in $3 x + 4 y = 19$ .

Subtract $4 y$ from both sides of the equation.

$3 x = 19 - 4 y$

$3 x + 6 y = 33$

Divide each term in $3 x = 19 - 4 y$ by $3$ and simplify.

Divide each term in $3 x = 19 - 4 y$ by $3$ .

$\frac{3 x}{3} = \frac{19}{3} + \frac{- 4 y}{3}$

$3 x + 6 y = 33$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{19}{3} + \frac{- 4 y}{3}$

$3 x + 6 y = 33$

Divide $x$ by $1$ .

$x = \frac{19}{3} + \frac{- 4 y}{3}$

$3 x + 6 y = 33$

$x = \frac{19}{3} + \frac{- 4 y}{3}$

$3 x + 6 y = 33$

$x = \frac{19}{3} + \frac{- 4 y}{3}$

$3 x + 6 y = 33$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{19}{3} - \frac{4 y}{3}$

$3 x + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$3 x + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$3 x + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$3 x + 6 y = 33$

Step 2

Replace all occurrences of $x$ with $\frac{19}{3} - \frac{4 y}{3}$ in each equation.

Replace all occurrences of $x$ in $3 x + 6 y = 33$ with $\frac{19}{3} - \frac{4 y}{3}$ .

$3 (\frac{19}{3} - \frac{4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Simplify the left side.

Simplify $3 (\frac{19}{3} - \frac{4 y}{3}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$3 (\frac{19}{3}) + 3 (- \frac{4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 (\frac{19}{3}) + 3 (- \frac{4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Rewrite the expression.

$19 + 3 (- \frac{4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$19 + 3 (- \frac{4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4 y}{3}$ into the numerator.

$19 + 3 (\frac{- 4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Cancel the common factor.

$19 + 3 (\frac{- 4 y}{3}) + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Rewrite the expression.

$19 - 4 y + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$19 - 4 y + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$19 - 4 y + 6 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Add $- 4 y$ and $6 y$ .

$19 + 2 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$19 + 2 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$19 + 2 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

$19 + 2 y = 33$

$x = \frac{19}{3} - \frac{4 y}{3}$

Step 3

Solve for $y$ in $19 + 2 y = 33$ .

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

Subtract $19$ from both sides of the equation.

$2 y = 33 - 19$

$x = \frac{19}{3} - \frac{4 y}{3}$

Subtract $19$ from $33$ .

$2 y = 14$

$x = \frac{19}{3} - \frac{4 y}{3}$

$2 y = 14$

$x = \frac{19}{3} - \frac{4 y}{3}$

Divide each term in $2 y = 14$ by $2$ and simplify.

Divide each term in $2 y = 14$ by $2$ .

$\frac{2 y}{2} = \frac{14}{2}$

$x = \frac{19}{3} - \frac{4 y}{3}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{14}{2}$

$x = \frac{19}{3} - \frac{4 y}{3}$

Divide $y$ by $1$ .

$y = \frac{14}{2}$

$x = \frac{19}{3} - \frac{4 y}{3}$

$y = \frac{14}{2}$

$x = \frac{19}{3} - \frac{4 y}{3}$

$y = \frac{14}{2}$

$x = \frac{19}{3} - \frac{4 y}{3}$

Simplify the right side.

Divide $14$ by $2$ .

$y = 7$

$x = \frac{19}{3} - \frac{4 y}{3}$

$y = 7$

$x = \frac{19}{3} - \frac{4 y}{3}$

$y = 7$

$x = \frac{19}{3} - \frac{4 y}{3}$

$y = 7$

$x = \frac{19}{3} - \frac{4 y}{3}$

Step 4

Replace all occurrences of $y$ with $7$ in each equation.

Replace all occurrences of $y$ in $x = \frac{19}{3} - \frac{4 y}{3}$ with $7$ .

$x = \frac{19}{3} - \frac{4 (7)}{3}$

$y = 7$

Simplify the right side.

Simplify $\frac{19}{3} - \frac{4 (7)}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{19 - 4 \cdot 7}{3}$

$y = 7$

Simplify the expression.

Multiply $- 4$ by $7$ .

$x = \frac{19 - 28}{3}$

$y = 7$

Subtract $28$ from $19$ .

$x = \frac{- 9}{3}$

$y = 7$

Divide $- 9$ by $3$ .

$x = - 3$

$y = 7$

$x = - 3$

$y = 7$

$x = - 3$

$y = 7$

$x = - 3$

$y = 7$

$x = - 3$

$y = 7$

Step 5

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

$(- 3, 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, 7)$

Equation Form:

$x = - 3, y = 7$

Step 7

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