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

$y = 2 x - 4$ , $7 x - 5 y = 14$

Step 1

Replace all occurrences of $y$ with $2 x - 4$ in each equation.

Replace all occurrences of $y$ in $7 x - 5 y = 14$ with $2 x - 4$ .

$7 x - 5 (2 x - 4) = 14$

$y = 2 x - 4$

Simplify the left side.

Simplify $7 x - 5 (2 x - 4)$ .

Simplify each term.

Apply the distributive property.

$7 x - 5 (2 x) - 5 \cdot - 4 = 14$

$y = 2 x - 4$

Multiply $2$ by $- 5$ .

$7 x - 10 x - 5 \cdot - 4 = 14$

$y = 2 x - 4$

Multiply $- 5$ by $- 4$ .

$7 x - 10 x + 20 = 14$

$y = 2 x - 4$

$7 x - 10 x + 20 = 14$

$y = 2 x - 4$

Subtract $10 x$ from $7 x$ .

$- 3 x + 20 = 14$

$y = 2 x - 4$

$- 3 x + 20 = 14$

$y = 2 x - 4$

$- 3 x + 20 = 14$

$y = 2 x - 4$

$- 3 x + 20 = 14$

$y = 2 x - 4$

Step 2

Solve for $x$ in $- 3 x + 20 = 14$ .

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

Subtract $20$ from both sides of the equation.

$- 3 x = 14 - 20$

$y = 2 x - 4$

Subtract $20$ from $14$ .

$- 3 x = - 6$

$y = 2 x - 4$

$- 3 x = - 6$

$y = 2 x - 4$

Divide each term in $- 3 x = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 6$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

$y = 2 x - 4$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

$y = 2 x - 4$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 3}$

$y = 2 x - 4$

$x = \frac{- 6}{- 3}$

$y = 2 x - 4$

$x = \frac{- 6}{- 3}$

$y = 2 x - 4$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x = 2$

$y = 2 x - 4$

$x = 2$

$y = 2 x - 4$

$x = 2$

$y = 2 x - 4$

$x = 2$

$y = 2 x - 4$

Step 3

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

Replace all occurrences of $x$ in $y = 2 x - 4$ with $2$ .

$y = 2 (2) - 4$

$x = 2$

Simplify the right side.

Simplify $2 (2) - 4$ .

Multiply $2$ by $2$ .

$y = 4 - 4$

$x = 2$

Subtract $4$ from $4$ .

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

Step 4

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

$(2, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 0)$

Equation Form:

$x = 2, y = 0$

Step 6

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

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