Solve the System of Equations -6x+8y=-10 and -4x+y=-11

$- 6 x + 8 y = - 10$ and $- 4 x + y = - 11$

Step 1

Add $4 x$ to both sides of the equation.

$y = - 11 + 4 x$

$- 6 x + 8 y = - 10$

Step 2

Replace all occurrences of $y$ with $- 11 + 4 x$ in each equation.

Replace all occurrences of $y$ in $- 6 x + 8 y = - 10$ with $- 11 + 4 x$ .

$- 6 x + 8 (- 11 + 4 x) = - 10$

$y = - 11 + 4 x$

Simplify the left side.

Simplify $- 6 x + 8 (- 11 + 4 x)$ .

Simplify each term.

Apply the distributive property.

$- 6 x + 8 \cdot - 11 + 8 (4 x) = - 10$

$y = - 11 + 4 x$

Multiply $8$ by $- 11$ .

$- 6 x - 88 + 8 (4 x) = - 10$

$y = - 11 + 4 x$

Multiply $4$ by $8$ .

$- 6 x - 88 + 32 x = - 10$

$y = - 11 + 4 x$

$- 6 x - 88 + 32 x = - 10$

$y = - 11 + 4 x$

Add $- 6 x$ and $32 x$ .

$26 x - 88 = - 10$

$y = - 11 + 4 x$

$26 x - 88 = - 10$

$y = - 11 + 4 x$

$26 x - 88 = - 10$

$y = - 11 + 4 x$

$26 x - 88 = - 10$

$y = - 11 + 4 x$

Step 3

Solve for $x$ in $26 x - 88 = - 10$ .

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

Add $88$ to both sides of the equation.

$26 x = - 10 + 88$

$y = - 11 + 4 x$

Add $- 10$ and $88$ .

$26 x = 78$

$y = - 11 + 4 x$

$26 x = 78$

$y = - 11 + 4 x$

Divide each term in $26 x = 78$ by $26$ and simplify.

Divide each term in $26 x = 78$ by $26$ .

$\frac{26 x}{26} = \frac{78}{26}$

$y = - 11 + 4 x$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{78}{26}$

$y = - 11 + 4 x$

Divide $x$ by $1$ .

$x = \frac{78}{26}$

$y = - 11 + 4 x$

$x = \frac{78}{26}$

$y = - 11 + 4 x$

$x = \frac{78}{26}$

$y = - 11 + 4 x$

Simplify the right side.

Divide $78$ by $26$ .

$x = 3$

$y = - 11 + 4 x$

$x = 3$

$y = - 11 + 4 x$

$x = 3$

$y = - 11 + 4 x$

$x = 3$

$y = - 11 + 4 x$

Step 4

Replace all occurrences of $x$ with $3$ in each equation.

Replace all occurrences of $x$ in $y = - 11 + 4 x$ with $3$ .

$y = - 11 + 4 (3)$

$x = 3$

Simplify the right side.

Simplify $- 11 + 4 (3)$ .

Multiply $4$ by $3$ .

$y = - 11 + 12$

$x = 3$

Add $- 11$ and $12$ .

$y = 1$

$x = 3$

$y = 1$

$x = 3$

$y = 1$

$x = 3$

$y = 1$

$x = 3$

Step 5

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

$(3, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Step 7

Solve the System of Equations -6x+8y=-10 and -4x+y=-11

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