Solve by Substitution x+7y=33 3x-2y=7

$x + 7 y = 33$ $3 x - 2 y = 7$

Step 1

Subtract $7 y$ from both sides of the equation.

$x = 33 - 7 y$

$3 x - 2 y = 7$

Step 2

Replace all occurrences of $x$ with $33 - 7 y$ in each equation.

Replace all occurrences of $x$ in $3 x - 2 y = 7$ with $33 - 7 y$ .

$3 (33 - 7 y) - 2 y = 7$

$x = 33 - 7 y$

Simplify the left side.

Simplify $3 (33 - 7 y) - 2 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 33 + 3 (- 7 y) - 2 y = 7$

$x = 33 - 7 y$

Multiply $3$ by $33$ .

$99 + 3 (- 7 y) - 2 y = 7$

$x = 33 - 7 y$

Multiply $- 7$ by $3$ .

$99 - 21 y - 2 y = 7$

$x = 33 - 7 y$

$99 - 21 y - 2 y = 7$

$x = 33 - 7 y$

Subtract $2 y$ from $- 21 y$ .

$99 - 23 y = 7$

$x = 33 - 7 y$

$99 - 23 y = 7$

$x = 33 - 7 y$

$99 - 23 y = 7$

$x = 33 - 7 y$

$99 - 23 y = 7$

$x = 33 - 7 y$

Step 3

Solve for $y$ in $99 - 23 y = 7$ .

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

Subtract $99$ from both sides of the equation.

$- 23 y = 7 - 99$

$x = 33 - 7 y$

Subtract $99$ from $7$ .

$- 23 y = - 92$

$x = 33 - 7 y$

$- 23 y = - 92$

$x = 33 - 7 y$

Divide each term in $- 23 y = - 92$ by $- 23$ and simplify.

Divide each term in $- 23 y = - 92$ by $- 23$ .

$\frac{- 23 y}{- 23} = \frac{- 92}{- 23}$

$x = 33 - 7 y$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 y}{- 23} = \frac{- 92}{- 23}$

$x = 33 - 7 y$

Divide $y$ by $1$ .

$y = \frac{- 92}{- 23}$

$x = 33 - 7 y$

$y = \frac{- 92}{- 23}$

$x = 33 - 7 y$

$y = \frac{- 92}{- 23}$

$x = 33 - 7 y$

Simplify the right side.

Divide $- 92$ by $- 23$ .

$y = 4$

$x = 33 - 7 y$

$y = 4$

$x = 33 - 7 y$

$y = 4$

$x = 33 - 7 y$

$y = 4$

$x = 33 - 7 y$

Step 4

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = 33 - 7 y$ with $4$ .

$x = 33 - 7 \cdot 4$

$y = 4$

Simplify the right side.

Simplify $33 - 7 \cdot 4$ .

Multiply $- 7$ by $4$ .

$x = 33 - 28$

$y = 4$

Subtract $28$ from $33$ .

$x = 5$

$y = 4$

$x = 5$

$y = 4$

$x = 5$

$y = 4$

$x = 5$

$y = 4$

Step 5

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

$(5, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 4)$

Equation Form:

$x = 5, y = 4$

Step 7

Solve by Substitution x+7y=33 3x-2y=7

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