Solve by Substitution 5x-2y=18 , 3x+3y=15

$5 x - 2 y = 18$ , $3 x + 3 y = 15$

Step 1

Solve for $x$ in $5 x - 2 y = 18$ .

Add $2 y$ to both sides of the equation.

$5 x = 18 + 2 y$

$3 x + 3 y = 15$

Divide each term in $5 x = 18 + 2 y$ by $5$ and simplify.

Divide each term in $5 x = 18 + 2 y$ by $5$ .

$\frac{5 x}{5} = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

Divide $x$ by $1$ .

$x = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$3 x + 3 y = 15$

Step 2

Replace all occurrences of $x$ with $\frac{18}{5} + \frac{2 y}{5}$ in each equation.

Replace all occurrences of $x$ in $3 x + 3 y = 15$ with $\frac{18}{5} + \frac{2 y}{5}$ .

$3 (\frac{18}{5} + \frac{2 y}{5}) + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Simplify the left side.

Simplify $3 (\frac{18}{5} + \frac{2 y}{5}) + 3 y$ .

Simplify each term.

Apply the distributive property.

$3 (\frac{18}{5}) + 3 (\frac{2 y}{5}) + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Multiply $3 (\frac{18}{5})$ .

Combine $3$ and $\frac{18}{5}$ .

$\frac{3 \cdot 18}{5} + 3 (\frac{2 y}{5}) + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Multiply $3$ by $18$ .

$\frac{54}{5} + 3 (\frac{2 y}{5}) + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{54}{5} + 3 (\frac{2 y}{5}) + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Multiply $3 \frac{2 y}{5}$ .

Combine $3$ and $\frac{2 y}{5}$ .

$\frac{54}{5} + \frac{3 (2 y)}{5} + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Multiply $2$ by $3$ .

$\frac{54}{5} + \frac{6 y}{5} + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{54}{5} + \frac{6 y}{5} + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{54}{5} + \frac{6 y}{5} + 3 y = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{54}{5} + \frac{6 y}{5} + 3 y \cdot \frac{5}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

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

$\frac{54}{5} + \frac{6 y}{5} + \frac{3 y \cdot 5}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Combine the numerators over the common denominator.

$\frac{54}{5} + \frac{6 y + 3 y \cdot 5}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Combine the numerators over the common denominator.

$\frac{54 + 6 y + 3 y \cdot 5}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Multiply $5$ by $3$ .

$\frac{54 + 6 y + 15 y}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Add $6 y$ and $15 y$ .

$\frac{54 + 21 y}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Factor $3$ out of $54 + 21 y$ .

Factor $3$ out of $54$ .

$\frac{3 (18) + 21 y}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Factor $3$ out of $21 y$ .

$\frac{3 (18) + 3 (7 y)}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Factor $3$ out of $3 (18) + 3 (7 y)$ .

$\frac{3 (18 + 7 y)}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{3 (18 + 7 y)}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{3 (18 + 7 y)}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{3 (18 + 7 y)}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

$\frac{3 (18 + 7 y)}{5} = 15$

$x = \frac{18}{5} + \frac{2 y}{5}$

Step 3

Solve for $y$ in $\frac{3 (18 + 7 y)}{5} = 15$ .

Multiply both sides by $5$ .

$\frac{3 (18 + 7 y)}{5} \cdot 5 = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Simplify.

Simplify the left side.

Simplify $\frac{3 (18 + 7 y)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3 (18 + 7 y)}{5} \cdot 5 = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Rewrite the expression.

$3 (18 + 7 y) = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

$3 (18 + 7 y) = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Apply the distributive property.

$3 \cdot 18 + 3 (7 y) = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Simplify the expression.

Multiply $3$ by $18$ .

$54 + 3 (7 y) = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Multiply $7$ by $3$ .

$54 + 21 y = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Reorder $54$ and $21 y$ .

$21 y + 54 = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

$21 y + 54 = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

$21 y + 54 = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

$21 y + 54 = 15 \cdot 5$

$x = \frac{18}{5} + \frac{2 y}{5}$

Simplify the right side.

Multiply $15$ by $5$ .

$21 y + 54 = 75$

$x = \frac{18}{5} + \frac{2 y}{5}$

$21 y + 54 = 75$

$x = \frac{18}{5} + \frac{2 y}{5}$

$21 y + 54 = 75$

$x = \frac{18}{5} + \frac{2 y}{5}$

Solve for $y$ .

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

Subtract $54$ from both sides of the equation.

$21 y = 75 - 54$

$x = \frac{18}{5} + \frac{2 y}{5}$

Subtract $54$ from $75$ .

$21 y = 21$

$x = \frac{18}{5} + \frac{2 y}{5}$

$21 y = 21$

$x = \frac{18}{5} + \frac{2 y}{5}$

Divide each term in $21 y = 21$ by $21$ and simplify.

Divide each term in $21 y = 21$ by $21$ .

$\frac{21 y}{21} = \frac{21}{21}$

$x = \frac{18}{5} + \frac{2 y}{5}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 y}{21} = \frac{21}{21}$

$x = \frac{18}{5} + \frac{2 y}{5}$

Divide $y$ by $1$ .

$y = \frac{21}{21}$

$x = \frac{18}{5} + \frac{2 y}{5}$

$y = \frac{21}{21}$

$x = \frac{18}{5} + \frac{2 y}{5}$

$y = \frac{21}{21}$

$x = \frac{18}{5} + \frac{2 y}{5}$

Simplify the right side.

Divide $21$ by $21$ .

$y = 1$

$x = \frac{18}{5} + \frac{2 y}{5}$

$y = 1$

$x = \frac{18}{5} + \frac{2 y}{5}$

$y = 1$

$x = \frac{18}{5} + \frac{2 y}{5}$

$y = 1$

$x = \frac{18}{5} + \frac{2 y}{5}$

$y = 1$

$x = \frac{18}{5} + \frac{2 y}{5}$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{18}{5} + \frac{2 y}{5}$ with $1$ .

$x = \frac{18}{5} + \frac{2 (1)}{5}$

$y = 1$

Simplify the right side.

Simplify $\frac{18}{5} + \frac{2 (1)}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{18 + 2 (1)}{5}$

$y = 1$

Simplify the expression.

Multiply $2$ by $1$ .

$x = \frac{18 + 2}{5}$

$y = 1$

Add $18$ and $2$ .

$x = \frac{20}{5}$

$y = 1$

Divide $20$ by $5$ .

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

Step 5

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

$(4, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 1)$

Equation Form:

$x = 4, y = 1$

Step 7

Solve by Substitution 5x-2y=18 , 3x+3y=15

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