Solve the System of Equations 5x+6y=26 and -x+y=-14

$5 x + 6 y = 26$ and $- x + y = - 14$

Step 1

Add $x$ to both sides of the equation.

$y = - 14 + x$

$5 x + 6 y = 26$

Step 2

Replace all occurrences of $y$ with $- 14 + x$ in each equation.

Replace all occurrences of $y$ in $5 x + 6 y = 26$ with $- 14 + x$ .

$5 x + 6 (- 14 + x) = 26$

$y = - 14 + x$

Simplify the left side.

Simplify $5 x + 6 (- 14 + x)$ .

Simplify each term.

Apply the distributive property.

$5 x + 6 \cdot - 14 + 6 x = 26$

$y = - 14 + x$

Multiply $6$ by $- 14$ .

$5 x - 84 + 6 x = 26$

$y = - 14 + x$

$5 x - 84 + 6 x = 26$

$y = - 14 + x$

Add $5 x$ and $6 x$ .

$11 x - 84 = 26$

$y = - 14 + x$

$11 x - 84 = 26$

$y = - 14 + x$

$11 x - 84 = 26$

$y = - 14 + x$

$11 x - 84 = 26$

$y = - 14 + x$

Step 3

Solve for $x$ in $11 x - 84 = 26$ .

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

Add $84$ to both sides of the equation.

$11 x = 26 + 84$

$y = - 14 + x$

Add $26$ and $84$ .

$11 x = 110$

$y = - 14 + x$

$11 x = 110$

$y = - 14 + x$

Divide each term in $11 x = 110$ by $11$ and simplify.

Divide each term in $11 x = 110$ by $11$ .

$\frac{11 x}{11} = \frac{110}{11}$

$y = - 14 + x$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{110}{11}$

$y = - 14 + x$

Divide $x$ by $1$ .

$x = \frac{110}{11}$

$y = - 14 + x$

$x = \frac{110}{11}$

$y = - 14 + x$

$x = \frac{110}{11}$

$y = - 14 + x$

Simplify the right side.

Divide $110$ by $11$ .

$x = 10$

$y = - 14 + x$

$x = 10$

$y = - 14 + x$

$x = 10$

$y = - 14 + x$

$x = 10$

$y = - 14 + x$

Step 4

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

Replace all occurrences of $x$ in $y = - 14 + x$ with $10$ .

$y = - 14 + 10$

$x = 10$

Simplify $y = - 14 + 10$ .

Simplify the left side.

Remove parentheses.

$y = - 14 + 10$

$x = 10$

$y = - 14 + 10$

$x = 10$

Simplify the right side.

Add $- 14$ and $10$ .

$y = - 4$

$x = 10$

$y = - 4$

$x = 10$

$y = - 4$

$x = 10$

$y = - 4$

$x = 10$

Step 5

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

$(10, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(10, - 4)$

Equation Form:

$x = 10, y = - 4$

Step 7

Solve the System of Equations 5x+6y=26 and -x+y=-14

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