Solve by Substitution y=2x+9 , y=7x+10

$y = 2 x + 9$ , $y = 7 x + 10$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x + 9 = 7 x + 10$

Step 2

Solve $2 x + 9 = 7 x + 10$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $7 x$ from both sides of the equation.

$2 x + 9 - 7 x = 10$

Subtract $7 x$ from $2 x$ .

$- 5 x + 9 = 10$

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

Subtract $9$ from both sides of the equation.

$- 5 x = 10 - 9$

Subtract $9$ from $10$ .

$- 5 x = 1$

Divide each term in $- 5 x = 1$ by $- 5$ and simplify.

Divide each term in $- 5 x = 1$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{1}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{1}{- 5}$

Divide $x$ by $1$ .

$x = \frac{1}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

Step 3

Evaluate $y$ when $x = - \frac{1}{5}$ .

Substitute $- \frac{1}{5}$ for $x$ .

$y = 7 (- \frac{1}{5}) + 10$

Simplify $7 (- \frac{1}{5}) + 10$ .

Simplify each term.

Multiply $7 (- \frac{1}{5})$ .

Multiply $- 1$ by $7$ .

$y = - 7 (\frac{1}{5}) + 10$

Combine $- 7$ and $\frac{1}{5}$ .

$y = \frac{- 7}{5} + 10$

Move the negative in front of the fraction.

$y = - \frac{7}{5} + 10$

To write $10$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{7}{5} + 10 \cdot \frac{5}{5}$

Combine $10$ and $\frac{5}{5}$ .

$y = - \frac{7}{5} + \frac{10 \cdot 5}{5}$

Combine the numerators over the common denominator.

$y = \frac{- 7 + 10 \cdot 5}{5}$

Simplify the numerator.

Multiply $10$ by $5$ .

$y = \frac{- 7 + 50}{5}$

Add $- 7$ and $50$ .

$y = \frac{43}{5}$

Step 4

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

$(- \frac{1}{5}, \frac{43}{5})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{1}{5}, \frac{43}{5})$

Equation Form:

$x = - \frac{1}{5}, y = \frac{43}{5}$

Step 6

Solve by Substitution y=2x+9 , y=7x+10

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