Solve by Substitution three x plus three y equals twenty-one , four x plus two y equals eighteen

$3 x + 3 y = 21$ , $4 x + 2 y = 18$

Calculate $x$ in the Initially equation.

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

$3 x = 21 - 3 y$

$4 x + 2 y = 18$

First, divide each term by $3$ and Clarify.

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Divide each term in $3 x = 21 - 3 y$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3} + \frac{- 3 y}{3}$

$4 x + 2 y = 18$

The common factor should be canceled of $3$ .

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Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3} + \frac{- 3 y}{3}$

$4 x + 2 y = 18$

Divide $x$ by $1$ .

$x = \frac{21}{3} + \frac{- 3 y}{3}$

$4 x + 2 y = 18$

$x = \frac{21}{3} + \frac{- 3 y}{3}$

$4 x + 2 y = 18$

Clarify each term.

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Divide $21$ by $3$ .

$x = 7 + \frac{- 3 y}{3}$

$4 x + 2 y = 18$

The common factor $- 3$ should be canceled and $3$ .

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Factor $3$ out of $- 3 y$ .

$x = 7 + \frac{3 (- y)}{3}$

$4 x + 2 y = 18$

The common factors should be canceled.

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Factor $3$ out of $3$ .

$x = 7 + \frac{3 (- y)}{3 (1)}$

$4 x + 2 y = 18$

Cancel the common factor.

$x = 7 + \frac{3 (- y)}{3 \cdot 1}$

$4 x + 2 y = 18$

Reformulate the expression.

$x = 7 + \frac{- y}{1}$

$4 x + 2 y = 18$

Divide $- y$ by $1$ .

$x = 7 - y$

$4 x + 2 y = 18$

$x = 7 - y$

$4 x + 2 y = 18$

$x = 7 - y$

$4 x + 2 y = 18$

$x = 7 - y$

$4 x + 2 y = 18$

$x = 7 - y$

$4 x + 2 y = 18$

$x = 7 - y$

$4 x + 2 y = 18$

Replace all occurrences of $x$ in $4 x + 2 y = 18$ with $7 - y$ .

$x = 7 - y$

$4 (7 - y) + 2 y = 18$

Simplify $4 (7 - y) + 2 y$ .

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Simplify each term.

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Use the distributive law.

$x = 7 - y$

$4 \cdot 7 + 4 (- y) + 2 y = 18$

First, multiply $4$ by $7$ .

$x = 7 - y$

$28 + 4 (- y) + 2 y = 18$

Multiply $- 1$ by $4$ .

$x = 7 - y$

$28 - 4 y + 2 y = 18$

$x = 7 - y$

$28 - 4 y + 2 y = 18$

Add $- 4 y$ and $2 y$ .

$x = 7 - y$

$28 - 2 y = 18$

$x = 7 - y$

$28 - 2 y = 18$

Calculate $y$ in the second equation.

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

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Subtract $28$ from both sides of the equation.

$x = 7 - y$

$- 2 y = 18 - 28$

Subtract $28$ from $18$ .

$x = 7 - y$

$- 2 y = - 10$

$x = 7 - y$

$- 2 y = - 10$

Divide each term by $- 2$ and simplify.

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Divide each term in $- 2 y = - 10$ by $- 2$ .

$x = 7 - y$

$\frac{- 2 y}{- 2} = \frac{- 10}{- 2}$

The common factor $- 2$ should be canceled.

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Cancel the common factor.

$x = 7 - y$

$\frac{- 2 y}{- 2} = \frac{- 10}{- 2}$

Divide $y$ by $1$ .

$x = 7 - y$

$y = \frac{- 10}{- 2}$

$x = 7 - y$

$y = \frac{- 10}{- 2}$

Divide $- 10$ by $- 2$ .

$x = 7 - y$

$y = 5$

$x = 7 - y$

$y = 5$

$x = 7 - y$

$y = 5$

Replace all occurrences of $y$ in $x = 7 - y$ with $5$ .

$x = 7 - (5)$

$y = 5$

Simplify $7 - (5)$ .

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Multiply $- 1$ by $5$ .

$x = 7 - 5$

$y = 5$

Subtract $5$ from $7$ .

$x = 2$

$y = 5$

$x = 2$

$y = 5$

The solution to the system of equations can be represented as a point.

$(2, 5)$

The result can be displayed in a variety of ways.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

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