Solve the System of Equations 10x-y=53 y=(-13x+92)/2

$10 x - y = 53$ $y = \frac{- 13 x + 92}{2}$

Simplify $\frac{- 13 x + 92}{2}$ .

Factor $- 1$ out of $- 13 x$ .

$y = \frac{- (13 x) + 92}{2}$

$10 x - y = 53$

Rewrite $92$ as $- 1 (- 92)$ .

$y = \frac{- (13 x) - 1 \cdot - 92}{2}$

$10 x - y = 53$

Factor $- 1$ out of $- (13 x) - 1 (- 92)$ .

$y = \frac{- (13 x - 92)}{2}$

$10 x - y = 53$

Simplify the expression.

Rewrite $- (13 x - 92)$ as $- 1 (13 x - 92)$ .

$y = \frac{- 1 (13 x - 92)}{2}$

$10 x - y = 53$

Move the negative in front of the fraction.

$y = - \frac{13 x - 92}{2}$

$10 x - y = 53$

$y = - \frac{13 x - 92}{2}$

$10 x - y = 53$

$y = - \frac{13 x - 92}{2}$

$10 x - y = 53$

Replace all occurrences of $y$ with $- \frac{13 x - 92}{2}$ in each equation.

Replace all occurrences of $y$ in $10 x - y = 53$ with $- \frac{13 x - 92}{2}$ .

$10 x - (- \frac{13 x - 92}{2}) = 53$

$y = - \frac{13 x - 92}{2}$

Simplify the left side.

Simplify $10 x - (- \frac{13 x - 92}{2})$ .

Multiply $- (- \frac{13 x - 92}{2})$ .

Multiply $- 1$ by $- 1$ .

$10 x + 1 (\frac{13 x - 92}{2}) = 53$

$y = - \frac{13 x - 92}{2}$

Multiply $\frac{13 x - 92}{2}$ by $1$ .

$10 x + \frac{13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

$10 x + \frac{13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

To write $10 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$10 x \cdot \frac{2}{2} + \frac{13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

Simplify terms.

Combine $10 x$ and $\frac{2}{2}$ .

$\frac{10 x \cdot 2}{2} + \frac{13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

Combine the numerators over the common denominator.

$\frac{10 x \cdot 2 + 13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

$\frac{10 x \cdot 2 + 13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

Simplify the numerator.

Multiply $2$ by $10$ .

$\frac{20 x + 13 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

Add $20 x$ and $13 x$ .

$\frac{33 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

$\frac{33 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

$\frac{33 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

$\frac{33 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

$\frac{33 x - 92}{2} = 53$

$y = - \frac{13 x - 92}{2}$

Solve for $x$ in $\frac{33 x - 92}{2} = 53$ .

Multiply both sides by $2$ .

$\frac{33 x - 92}{2} \cdot 2 = 53 \cdot 2$

$y = - \frac{13 x - 92}{2}$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{33 x - 92}{2} \cdot 2 = 53 \cdot 2$

$y = - \frac{13 x - 92}{2}$

Rewrite the expression.

$33 x - 92 = 53 \cdot 2$

$y = - \frac{13 x - 92}{2}$

$33 x - 92 = 53 \cdot 2$

$y = - \frac{13 x - 92}{2}$

$33 x - 92 = 53 \cdot 2$

$y = - \frac{13 x - 92}{2}$

Simplify the right side.

Multiply $53$ by $2$ .

$33 x - 92 = 106$

$y = - \frac{13 x - 92}{2}$

$33 x - 92 = 106$

$y = - \frac{13 x - 92}{2}$

$33 x - 92 = 106$

$y = - \frac{13 x - 92}{2}$

Solve for $x$ .

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

Add $92$ to both sides of the equation.

$33 x = 106 + 92$

$y = - \frac{13 x - 92}{2}$

Add $106$ and $92$ .

$33 x = 198$

$y = - \frac{13 x - 92}{2}$

$33 x = 198$

$y = - \frac{13 x - 92}{2}$

Divide each term in $33 x = 198$ by $33$ and simplify.

Divide each term in $33 x = 198$ by $33$ .

$\frac{33 x}{33} = \frac{198}{33}$

$y = - \frac{13 x - 92}{2}$

Simplify the left side.

Cancel the common factor of $33$ .

Cancel the common factor.

$\frac{33 x}{33} = \frac{198}{33}$

$y = - \frac{13 x - 92}{2}$

Divide $x$ by $1$ .

$x = \frac{198}{33}$

$y = - \frac{13 x - 92}{2}$

$x = \frac{198}{33}$

$y = - \frac{13 x - 92}{2}$

$x = \frac{198}{33}$

$y = - \frac{13 x - 92}{2}$

Simplify the right side.

Divide $198$ by $33$ .

$x = 6$

$y = - \frac{13 x - 92}{2}$

$x = 6$

$y = - \frac{13 x - 92}{2}$

$x = 6$

$y = - \frac{13 x - 92}{2}$

$x = 6$

$y = - \frac{13 x - 92}{2}$

$x = 6$

$y = - \frac{13 x - 92}{2}$

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

Replace all occurrences of $x$ in $y = - \frac{13 x - 92}{2}$ with $6$ .

$y = - \frac{13 (6) - 92}{2}$

$x = 6$

Simplify the right side.

Simplify $- \frac{13 (6) - 92}{2}$ .

Cancel the common factor of $13 (6) - 92$ and $2$ .

Factor $2$ out of $13 (6)$ .

$y = - \frac{2 (13 \cdot (3)) - 92}{2}$

$x = 6$

Factor $2$ out of $- 92$ .

$y = - \frac{2 (13 \cdot (3)) + 2 \cdot - 46}{2}$

$x = 6$

Factor $2$ out of $2 (13 \cdot (3)) + 2 (- 46)$ .

$y = - \frac{2 (13 \cdot (3) - 46)}{2}$

$x = 6$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = - \frac{2 (13 \cdot (3) - 46)}{2 (1)}$

$x = 6$

Cancel the common factor.

$y = - \frac{2 (13 \cdot (3) - 46)}{2 \cdot 1}$

$x = 6$

Rewrite the expression.

$y = - \frac{13 \cdot (3) - 46}{1}$

$x = 6$

Divide $13 \cdot (3) - 46$ by $1$ .

$y = - (13 \cdot (3) - 46)$

$x = 6$

$y = - (13 \cdot (3) - 46)$

$x = 6$

$y = - (13 \cdot (3) - 46)$

$x = 6$

Multiply $13$ by $3$ .

$y = - (39 - 46)$

$x = 6$

Simplify the expression.

Subtract $46$ from $39$ .

$y = 7$

$x = 6$

Multiply $- 1$ by $- 7$ .

$y = 7$

$x = 6$

$y = 7$

$x = 6$

$y = 7$

$x = 6$

$y = 7$

$x = 6$

$y = 7$

$x = 6$

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

$(6, 7)$

The result can be shown in multiple forms.

Point Form:

$(6, 7)$

Equation Form:

$x = 6, y = 7$

Solve the System of Equations 10x-y=53 y=(-13x+92)/2

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