Solve by Substitution 2x+3y=5 , 4x+6y=10

$2 x + 3 y = 5$ , $4 x + 6 y = 10$

Step 1

Solve for $x$ in $2 x + 3 y = 5$ .

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

$2 x = 5 - 3 y$

$4 x + 6 y = 10$

Divide each term in $2 x = 5 - 3 y$ by $2$ and simplify.

Divide each term in $2 x = 5 - 3 y$ by $2$ .

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

$4 x + 6 y = 10$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$4 x + 6 y = 10$

Divide $x$ by $1$ .

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

$4 x + 6 y = 10$

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

$4 x + 6 y = 10$

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

$4 x + 6 y = 10$

Simplify the right side.

Move the negative in front of the fraction.

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

$4 x + 6 y = 10$

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

$4 x + 6 y = 10$

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

$4 x + 6 y = 10$

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

$4 x + 6 y = 10$

Step 2

Replace all occurrences of $x$ with $\frac{5}{2} - \frac{3 y}{2}$ in each equation.

Replace all occurrences of $x$ in $4 x + 6 y = 10$ with $\frac{5}{2} - \frac{3 y}{2}$ .

$4 (\frac{5}{2} - \frac{3 y}{2}) + 6 y = 10$

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

Simplify the left side.

Simplify $4 (\frac{5}{2} - \frac{3 y}{2}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{5}{2}) + 4 (- \frac{3 y}{2}) + 6 y = 10$

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) (\frac{5}{2}) + 4 (- \frac{3 y}{2}) + 6 y = 10$

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

Cancel the common factor.

$2 \cdot (2 (\frac{5}{2})) + 4 (- \frac{3 y}{2}) + 6 y = 10$

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

Rewrite the expression.

$2 \cdot 5 + 4 (- \frac{3 y}{2}) + 6 y = 10$

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

$2 \cdot 5 + 4 (- \frac{3 y}{2}) + 6 y = 10$

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

Multiply $2$ by $5$ .

$10 + 4 (- \frac{3 y}{2}) + 6 y = 10$

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 y}{2}$ into the numerator.

$10 + 4 (\frac{- 3 y}{2}) + 6 y = 10$

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

Factor $2$ out of $4$ .

$10 + 2 (2) (\frac{- 3 y}{2}) + 6 y = 10$

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

Cancel the common factor.

$10 + 2 \cdot (2 (\frac{- 3 y}{2})) + 6 y = 10$

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

Rewrite the expression.

$10 + 2 (- 3 y) + 6 y = 10$

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

$10 + 2 (- 3 y) + 6 y = 10$

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

Multiply $- 3$ by $2$ .

$10 - 6 y + 6 y = 10$

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

$10 - 6 y + 6 y = 10$

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

Combine the opposite terms in $10 - 6 y + 6 y$ .

Add $- 6 y$ and $6 y$ .

$10 + 0 = 10$

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

Add $10$ and $0$ .

$10 = 10$

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

$10 = 10$

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

$10 = 10$

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

$10 = 10$

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

$10 = 10$

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

Step 3

Remove any equations from the system that are always true.

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

Step 4

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