Solve by Substitution 5x+2y=7 , 10x+4y=14

$5 x + 2 y = 7$ , $10 x + 4 y = 14$

Step 1

Solve for $x$ in $5 x + 2 y = 7$ .

Subtract $2 y$ from both sides of the equation.

$5 x = 7 - 2 y$

$10 x + 4 y = 14$

Divide each term in $5 x = 7 - 2 y$ by $5$ and simplify.

Divide each term in $5 x = 7 - 2 y$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5} + \frac{- 2 y}{5}$

$10 x + 4 y = 14$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5} + \frac{- 2 y}{5}$

$10 x + 4 y = 14$

Divide $x$ by $1$ .

$x = \frac{7}{5} + \frac{- 2 y}{5}$

$10 x + 4 y = 14$

$x = \frac{7}{5} + \frac{- 2 y}{5}$

$10 x + 4 y = 14$

$x = \frac{7}{5} + \frac{- 2 y}{5}$

$10 x + 4 y = 14$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{7}{5} - \frac{2 y}{5}$

$10 x + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$10 x + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$10 x + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$10 x + 4 y = 14$

Step 2

Replace all occurrences of $x$ with $\frac{7}{5} - \frac{2 y}{5}$ in each equation.

Replace all occurrences of $x$ in $10 x + 4 y = 14$ with $\frac{7}{5} - \frac{2 y}{5}$ .

$10 (\frac{7}{5} - \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Simplify the left side.

Simplify $10 (\frac{7}{5} - \frac{2 y}{5}) + 4 y$ .

Simplify each term.

Apply the distributive property.

$10 (\frac{7}{5}) + 10 (- \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$5 (2) (\frac{7}{5}) + 10 (- \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Cancel the common factor.

$5 \cdot (2 (\frac{7}{5})) + 10 (- \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Rewrite the expression.

$2 \cdot 7 + 10 (- \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$2 \cdot 7 + 10 (- \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Multiply $2$ by $7$ .

$14 + 10 (- \frac{2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2 y}{5}$ into the numerator.

$14 + 10 (\frac{- 2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Factor $5$ out of $10$ .

$14 + 5 (2) (\frac{- 2 y}{5}) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Cancel the common factor.

$14 + 5 \cdot (2 (\frac{- 2 y}{5})) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Rewrite the expression.

$14 + 2 (- 2 y) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$14 + 2 (- 2 y) + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Multiply $- 2$ by $2$ .

$14 - 4 y + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$14 - 4 y + 4 y = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Combine the opposite terms in $14 - 4 y + 4 y$ .

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

$14 + 0 = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Add $14$ and $0$ .

$14 = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$14 = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$14 = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$14 = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

$14 = 14$

$x = \frac{7}{5} - \frac{2 y}{5}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{7}{5} - \frac{2 y}{5}$

Step 4

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