Solve by Substitution (x+3y)/2=5 4-(2x-y)/2=1

$\frac{x + 3 y}{2} = 5$ $4 - \frac{2 x - y}{2} = 1$

Step 1

Solve for $x$ in $\frac{x + 3 y}{2} = 5$ .

Multiply both sides by $2$ .

$\frac{x + 3 y}{2} \cdot 2 = 5 \cdot 2$

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x + 3 y}{2} \cdot 2 = 5 \cdot 2$

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

Rewrite the expression.

$x + 3 y = 5 \cdot 2$

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

$x + 3 y = 5 \cdot 2$

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

$x + 3 y = 5 \cdot 2$

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

Simplify the right side.

Multiply $5$ by $2$ .

$x + 3 y = 10$

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

$x + 3 y = 10$

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

$x + 3 y = 10$

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

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

$x = 10 - 3 y$

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

$x = 10 - 3 y$

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

Step 2

Replace all occurrences of $x$ with $10 - 3 y$ in each equation.

Replace all occurrences of $x$ in $4 - \frac{2 x - y}{2} = 1$ with $10 - 3 y$ .

$4 - \frac{2 (10 - 3 y) - y}{2} = 1$

$x = 10 - 3 y$

Simplify the left side.

Simplify $4 - \frac{2 (10 - 3 y) - y}{2}$ .

Simplify the numerator.

Apply the distributive property.

$4 - \frac{2 \cdot 10 + 2 (- 3 y) - y}{2} = 1$

$x = 10 - 3 y$

Multiply $2$ by $10$ .

$4 - \frac{20 + 2 (- 3 y) - y}{2} = 1$

$x = 10 - 3 y$

Multiply $- 3$ by $2$ .

$4 - \frac{20 - 6 y - y}{2} = 1$

$x = 10 - 3 y$

Subtract $y$ from $- 6 y$ .

$4 - \frac{20 - 7 y}{2} = 1$

$x = 10 - 3 y$

$4 - \frac{20 - 7 y}{2} = 1$

$x = 10 - 3 y$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 \cdot \frac{2}{2} - \frac{20 - 7 y}{2} = 1$

$x = 10 - 3 y$

Simplify terms.

Combine $4$ and $\frac{2}{2}$ .

$\frac{4 \cdot 2}{2} - \frac{20 - 7 y}{2} = 1$

$x = 10 - 3 y$

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 - (20 - 7 y)}{2} = 1$

$x = 10 - 3 y$

$\frac{4 \cdot 2 - (20 - 7 y)}{2} = 1$

$x = 10 - 3 y$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{8 - (20 - 7 y)}{2} = 1$

$x = 10 - 3 y$

Apply the distributive property.

$\frac{8 - 1 \cdot 20 - (- 7 y)}{2} = 1$

$x = 10 - 3 y$

Multiply $- 1$ by $20$ .

$\frac{8 - 20 - (- 7 y)}{2} = 1$

$x = 10 - 3 y$

Multiply $- 7$ by $- 1$ .

$\frac{8 - 20 + 7 y}{2} = 1$

$x = 10 - 3 y$

Subtract $20$ from $8$ .

$\frac{- 12 + 7 y}{2} = 1$

$x = 10 - 3 y$

$\frac{- 12 + 7 y}{2} = 1$

$x = 10 - 3 y$

Simplify with factoring out.

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- 1 \cdot 12 + 7 y}{2} = 1$

$x = 10 - 3 y$

Factor $- 1$ out of $7 y$ .

$\frac{- 1 \cdot 12 - (- 7 y)}{2} = 1$

$x = 10 - 3 y$

Factor $- 1$ out of $- 1 (12) - (- 7 y)$ .

$\frac{- 1 (12 - 7 y)}{2} = 1$

$x = 10 - 3 y$

Move the negative in front of the fraction.

$- \frac{12 - 7 y}{2} = 1$

$x = 10 - 3 y$

$- \frac{12 - 7 y}{2} = 1$

$x = 10 - 3 y$

$- \frac{12 - 7 y}{2} = 1$

$x = 10 - 3 y$

$- \frac{12 - 7 y}{2} = 1$

$x = 10 - 3 y$

$- \frac{12 - 7 y}{2} = 1$

$x = 10 - 3 y$

Step 3

Solve for $y$ in $- \frac{12 - 7 y}{2} = 1$ .

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{12 - 7 y}{2}) = - 2 \cdot 1$

$x = 10 - 3 y$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{12 - 7 y}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{12 - 7 y}{2}$ into the numerator.

$- 2 \frac{- (12 - 7 y)}{2} = - 2 \cdot 1$

$x = 10 - 3 y$

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (12 - 7 y)}{2}) = - 2 \cdot 1$

$x = 10 - 3 y$

Cancel the common factor.

$2 \cdot (- 1 \frac{- (12 - 7 y)}{2}) = - 2 \cdot 1$

$x = 10 - 3 y$

Rewrite the expression.

$12 - 7 y = - 2 \cdot 1$

$x = 10 - 3 y$

$12 - 7 y = - 2 \cdot 1$

$x = 10 - 3 y$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (12 - 7 y) = - 2 \cdot 1$

$x = 10 - 3 y$

Multiply $12 - 7 y$ by $1$ .

$12 - 7 y = - 2 \cdot 1$

$x = 10 - 3 y$

$12 - 7 y = - 2 \cdot 1$

$x = 10 - 3 y$

$12 - 7 y = - 2 \cdot 1$

$x = 10 - 3 y$

$12 - 7 y = - 2 \cdot 1$

$x = 10 - 3 y$

Simplify the right side.

Multiply $- 2$ by $1$ .

$12 - 7 y = - 2$

$x = 10 - 3 y$

$12 - 7 y = - 2$

$x = 10 - 3 y$

$12 - 7 y = - 2$

$x = 10 - 3 y$

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

Subtract $12$ from both sides of the equation.

$- 7 y = - 2 - 12$

$x = 10 - 3 y$

Subtract $12$ from $- 2$ .

$- 7 y = - 14$

$x = 10 - 3 y$

$- 7 y = - 14$

$x = 10 - 3 y$

Divide each term in $- 7 y = - 14$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 14$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 14}{- 7}$

$x = 10 - 3 y$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 14}{- 7}$

$x = 10 - 3 y$

Divide $y$ by $1$ .

$y = \frac{- 14}{- 7}$

$x = 10 - 3 y$

$y = \frac{- 14}{- 7}$

$x = 10 - 3 y$

$y = \frac{- 14}{- 7}$

$x = 10 - 3 y$

Simplify the right side.

Divide $- 14$ by $- 7$ .

$y = 2$

$x = 10 - 3 y$

$y = 2$

$x = 10 - 3 y$

$y = 2$

$x = 10 - 3 y$

$y = 2$

$x = 10 - 3 y$

Step 4

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = 10 - 3 y$ with $2$ .

$x = 10 - 3 \cdot 2$

$y = 2$

Simplify the right side.

Simplify $10 - 3 \cdot 2$ .

Multiply $- 3$ by $2$ .

$x = 10 - 6$

$y = 2$

Subtract $6$ from $10$ .

$x = 4$

$y = 2$

$x = 4$

$y = 2$

$x = 4$

$y = 2$

$x = 4$

$y = 2$

Step 5

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

$(4, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 7

Solve by Substitution (x+3y)/2=5 4-(2x-y)/2=1

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