Solve by Substitution 4x=3y-2 , 18=3x+y

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

Step 1

Divide each term in $4 x = 3 y - 2$ by $4$ and simplify.

Divide each term in $4 x = 3 y - 2$ by $4$ .

$\frac{4 x}{4} = \frac{3 y}{4} + \frac{- 2}{4}$

$18 = 3 x + y$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3 y}{4} + \frac{- 2}{4}$

$18 = 3 x + y$

Divide $x$ by $1$ .

$x = \frac{3 y}{4} + \frac{- 2}{4}$

$18 = 3 x + y$

$x = \frac{3 y}{4} + \frac{- 2}{4}$

$18 = 3 x + y$

$x = \frac{3 y}{4} + \frac{- 2}{4}$

$18 = 3 x + y$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

$x = \frac{3 y}{4} + \frac{2 (- 1)}{4}$

$18 = 3 x + y$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{3 y}{4} + \frac{2 \cdot - 1}{2 \cdot 2}$

$18 = 3 x + y$

Cancel the common factor.

$x = \frac{3 y}{4} + \frac{2 \cdot - 1}{2 \cdot 2}$

$18 = 3 x + y$

Rewrite the expression.

$x = \frac{3 y}{4} + \frac{- 1}{2}$

$18 = 3 x + y$

$x = \frac{3 y}{4} + \frac{- 1}{2}$

$18 = 3 x + y$

$x = \frac{3 y}{4} + \frac{- 1}{2}$

$18 = 3 x + y$

Move the negative in front of the fraction.

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = 3 x + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = 3 x + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = 3 x + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = 3 x + y$

Step 2

Replace all occurrences of $x$ with $\frac{3 y}{4} - \frac{1}{2}$ in each equation.

Replace all occurrences of $x$ in $18 = 3 x + y$ with $\frac{3 y}{4} - \frac{1}{2}$ .

$18 = 3 (\frac{3 y}{4} - \frac{1}{2}) + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

Simplify the right side.

Simplify $3 (\frac{3 y}{4} - \frac{1}{2}) + y$ .

Simplify each term.

Apply the distributive property.

$18 = 3 (\frac{3 y}{4}) + 3 (- \frac{1}{2}) + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

Multiply $3 \frac{3 y}{4}$ .

Combine $3$ and $\frac{3 y}{4}$ .

$18 = \frac{3 (3 y)}{4} + 3 (- \frac{1}{2}) + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

Multiply $3$ by $3$ .

$18 = \frac{9 y}{4} + 3 (- \frac{1}{2}) + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{9 y}{4} + 3 (- \frac{1}{2}) + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

Multiply $3 (- \frac{1}{2})$ .

Multiply $- 1$ by $3$ .

$18 = \frac{9 y}{4} - 3 (\frac{1}{2}) + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

Combine $- 3$ and $\frac{1}{2}$ .

$18 = \frac{9 y}{4} + \frac{- 3}{2} + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{9 y}{4} + \frac{- 3}{2} + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

Move the negative in front of the fraction.

$18 = \frac{9 y}{4} - \frac{3}{2} + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{9 y}{4} - \frac{3}{2} + y$

$x = \frac{3 y}{4} - \frac{1}{2}$

To write $y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$18 = \frac{9 y}{4} + y \cdot \frac{4}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Combine $y$ and $\frac{4}{4}$ .

$18 = \frac{9 y}{4} + \frac{y \cdot 4}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Combine the numerators over the common denominator.

$18 = \frac{9 y + y \cdot 4}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Add $9 y$ and $y \cdot 4$ .

Reorder $y$ and $4$ .

$18 = \frac{9 y + 4 \cdot y}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Add $9 y$ and $4 \cdot y$ .

$18 = \frac{13 y}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{13 y}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{13 y}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{13 y}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$18 = \frac{13 y}{4} - \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Step 3

Solve for $y$ in $18 = \frac{13 y}{4} - \frac{3}{2}$ .

Rewrite the equation as $\frac{13 y}{4} - \frac{3}{2} = 18$ .

$\frac{13 y}{4} - \frac{3}{2} = 18$

$x = \frac{3 y}{4} - \frac{1}{2}$

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

Add $\frac{3}{2}$ to both sides of the equation.

$\frac{13 y}{4} = 18 + \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

To write $18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13 y}{4} = 18 \cdot \frac{2}{2} + \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Combine $18$ and $\frac{2}{2}$ .

$\frac{13 y}{4} = \frac{18 \cdot 2}{2} + \frac{3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{13 y}{4} = \frac{18 \cdot 2 + 3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Simplify the numerator.

Multiply $18$ by $2$ .

$\frac{13 y}{4} = \frac{36 + 3}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Add $36$ and $3$ .

$\frac{13 y}{4} = \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$\frac{13 y}{4} = \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$\frac{13 y}{4} = \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Multiply both sides of the equation by $\frac{4}{13}$ .

$\frac{4}{13} \cdot \frac{13 y}{4} = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{13} \cdot \frac{13 y}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{13} \cdot \frac{13 y}{4} = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Rewrite the expression.

$\frac{1}{13} \cdot (13 y) = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$\frac{1}{13} \cdot (13 y) = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Cancel the common factor of $13$ .

Factor $13$ out of $13 y$ .

$\frac{1}{13} \cdot (13 (y)) = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Cancel the common factor.

$\frac{1}{13} \cdot (13 y) = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Rewrite the expression.

$y = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = \frac{4}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Simplify the right side.

Simplify $\frac{4}{13} \cdot \frac{39}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{2 (2)}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Cancel the common factor.

$y = \frac{2 \cdot 2}{13} \cdot \frac{39}{2}$

$x = \frac{3 y}{4} - \frac{1}{2}$

Rewrite the expression.

$y = \frac{2}{13} \cdot 39$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = \frac{2}{13} \cdot 39$

$x = \frac{3 y}{4} - \frac{1}{2}$

Cancel the common factor of $13$ .

Factor $13$ out of $39$ .

$y = \frac{2}{13} \cdot (13 (3))$

$x = \frac{3 y}{4} - \frac{1}{2}$

Cancel the common factor.

$y = \frac{2}{13} \cdot (13 \cdot 3)$

$x = \frac{3 y}{4} - \frac{1}{2}$

Rewrite the expression.

$y = 2 \cdot 3$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = 2 \cdot 3$

$x = \frac{3 y}{4} - \frac{1}{2}$

Multiply $2$ by $3$ .

$y = 6$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = 6$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = 6$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = 6$

$x = \frac{3 y}{4} - \frac{1}{2}$

$y = 6$

$x = \frac{3 y}{4} - \frac{1}{2}$

Step 4

Replace all occurrences of $y$ with $6$ in each equation.

Replace all occurrences of $y$ in $x = \frac{3 y}{4} - \frac{1}{2}$ with $6$ .

$x = \frac{3 (6)}{4} - \frac{1}{2}$

$y = 6$

Simplify the right side.

Simplify $\frac{3 (6)}{4} - \frac{1}{2}$ .

Multiply $3$ by $6$ .

$x = \frac{18}{4} - \frac{1}{2}$

$y = 6$

Cancel the common factor of $18$ and $4$ .

Factor $2$ out of $18$ .

$x = \frac{2 (9)}{4} - \frac{1}{2}$

$y = 6$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 9}{2 \cdot 2} - \frac{1}{2}$

$y = 6$

Cancel the common factor.

$x = \frac{2 \cdot 9}{2 \cdot 2} - \frac{1}{2}$

$y = 6$

Rewrite the expression.

$x = \frac{9}{2} - \frac{1}{2}$

$y = 6$

$x = \frac{9}{2} - \frac{1}{2}$

$y = 6$

$x = \frac{9}{2} - \frac{1}{2}$

$y = 6$

Combine the numerators over the common denominator.

$x = \frac{9 - 1}{2}$

$y = 6$

Simplify the expression.

Subtract $1$ from $9$ .

$x = \frac{8}{2}$

$y = 6$

Divide $8$ by $2$ .

$x = 4$

$y = 6$

$x = 4$

$y = 6$

$x = 4$

$y = 6$

$x = 4$

$y = 6$

$x = 4$

$y = 6$

Step 5

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

$(4, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 6)$

Equation Form:

$x = 4, y = 6$

Step 7

Solve by Substitution 4x=3y-2 , 18=3x+y

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