Solve by Substitution y=6x-11 and -2x-3y=-7

$y = 6 x - 11$ and $- 2 x - 3 y = - 7$

Step 1

Replace all occurrences of $y$ with $6 x - 11$ in each equation.

Replace all occurrences of $y$ in $- 2 x - 3 y = - 7$ with $6 x - 11$ .

$- 2 x - 3 (6 x - 11) = - 7$

$y = 6 x - 11$

Simplify the left side.

Simplify $- 2 x - 3 (6 x - 11)$ .

Simplify each term.

Apply the distributive property.

$- 2 x - 3 (6 x) - 3 \cdot - 11 = - 7$

$y = 6 x - 11$

Multiply $6$ by $- 3$ .

$- 2 x - 18 x - 3 \cdot - 11 = - 7$

$y = 6 x - 11$

Multiply $- 3$ by $- 11$ .

$- 2 x - 18 x + 33 = - 7$

$y = 6 x - 11$

$- 2 x - 18 x + 33 = - 7$

$y = 6 x - 11$

Subtract $18 x$ from $- 2 x$ .

$- 20 x + 33 = - 7$

$y = 6 x - 11$

$- 20 x + 33 = - 7$

$y = 6 x - 11$

$- 20 x + 33 = - 7$

$y = 6 x - 11$

$- 20 x + 33 = - 7$

$y = 6 x - 11$

Step 2

Solve for $x$ in $- 20 x + 33 = - 7$ .

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

Subtract $33$ from both sides of the equation.

$- 20 x = - 7 - 33$

$y = 6 x - 11$

Subtract $33$ from $- 7$ .

$- 20 x = - 40$

$y = 6 x - 11$

$- 20 x = - 40$

$y = 6 x - 11$

Divide each term in $- 20 x = - 40$ by $- 20$ and simplify.

Divide each term in $- 20 x = - 40$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 40}{- 20}$

$y = 6 x - 11$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 40}{- 20}$

$y = 6 x - 11$

Divide $x$ by $1$ .

$x = \frac{- 40}{- 20}$

$y = 6 x - 11$

$x = \frac{- 40}{- 20}$

$y = 6 x - 11$

$x = \frac{- 40}{- 20}$

$y = 6 x - 11$

Simplify the right side.

Divide $- 40$ by $- 20$ .

$x = 2$

$y = 6 x - 11$

$x = 2$

$y = 6 x - 11$

$x = 2$

$y = 6 x - 11$

$x = 2$

$y = 6 x - 11$

Step 3

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

Replace all occurrences of $x$ in $y = 6 x - 11$ with $2$ .

$y = 6 (2) - 11$

$x = 2$

Simplify the right side.

Simplify $6 (2) - 11$ .

Multiply $6$ by $2$ .

$y = 12 - 11$

$x = 2$

Subtract $11$ from $12$ .

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

Step 4

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

$(2, 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 6

Solve by Substitution y=6x-11 and -2x-3y=-7

Related Questions

Support LCMGCF.com by disabling your adblocker.