Solve the System of Equations x=y+10 7x+6y=5

$x = y + 10$ $7 x + 6 y = 5$

Step 1

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

Replace all occurrences of $x$ in $7 x + 6 y = 5$ with $y + 10$ .

$7 (y + 10) + 6 y = 5$

$x = y + 10$

Simplify the left side.

Simplify $7 (y + 10) + 6 y$ .

Simplify each term.

Apply the distributive property.

$7 y + 7 \cdot 10 + 6 y = 5$

$x = y + 10$

Multiply $7$ by $10$ .

$7 y + 70 + 6 y = 5$

$x = y + 10$

$7 y + 70 + 6 y = 5$

$x = y + 10$

Add $7 y$ and $6 y$ .

$13 y + 70 = 5$

$x = y + 10$

$13 y + 70 = 5$

$x = y + 10$

$13 y + 70 = 5$

$x = y + 10$

$13 y + 70 = 5$

$x = y + 10$

Step 2

Solve for $y$ in $13 y + 70 = 5$ .

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

Subtract $70$ from both sides of the equation.

$13 y = 5 - 70$

$x = y + 10$

Subtract $70$ from $5$ .

$13 y = - 65$

$x = y + 10$

$13 y = - 65$

$x = y + 10$

Divide each term in $13 y = - 65$ by $13$ and simplify.

Divide each term in $13 y = - 65$ by $13$ .

$\frac{13 y}{13} = \frac{- 65}{13}$

$x = y + 10$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 y}{13} = \frac{- 65}{13}$

$x = y + 10$

Divide $y$ by $1$ .

$y = \frac{- 65}{13}$

$x = y + 10$

$y = \frac{- 65}{13}$

$x = y + 10$

$y = \frac{- 65}{13}$

$x = y + 10$

Simplify the right side.

Divide $- 65$ by $13$ .

$y = - 5$

$x = y + 10$

$y = - 5$

$x = y + 10$

$y = - 5$

$x = y + 10$

$y = - 5$

$x = y + 10$

Step 3

Replace all occurrences of $y$ with $- 5$ in each equation.

Replace all occurrences of $y$ in $x = y + 10$ with $- 5$ .

$x = (- 5) + 10$

$y = - 5$

Simplify the right side.

Add $- 5$ and $10$ .

$x = 5$

$y = - 5$

$x = 5$

$y = - 5$

$x = 5$

$y = - 5$

Step 4

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

$(5, - 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(5, - 5)$

Equation Form:

$x = 5, y = - 5$

Step 6

Solve the System of Equations x=y+10 7x+6y=5

Related Questions

Support LCMGCF.com by disabling your adblocker.