Solve by Substitution 16x-10y=10 , -8x-6y=6

$16 x - 10 y = 10$ , $- 8 x - 6 y = 6$

Step 1

Solve for $x$ in $16 x - 10 y = 10$ .

Add $10 y$ to both sides of the equation.

$16 x = 10 + 10 y$

$- 8 x - 6 y = 6$

Divide each term in $16 x = 10 + 10 y$ by $16$ and simplify.

Divide each term in $16 x = 10 + 10 y$ by $16$ .

$\frac{16 x}{16} = \frac{10}{16} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{10}{16} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Divide $x$ by $1$ .

$x = \frac{10}{16} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

$x = \frac{10}{16} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

$x = \frac{10}{16} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $16$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{16} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Cancel the common factors.

Factor $2$ out of $16$ .

$x = \frac{2 \cdot 5}{2 \cdot 8} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 8} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Rewrite the expression.

$x = \frac{5}{8} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{10 y}{16}$

$- 8 x - 6 y = 6$

Cancel the common factor of $10$ and $16$ .

Factor $2$ out of $10 y$ .

$x = \frac{5}{8} + \frac{2 (5 y)}{16}$

$- 8 x - 6 y = 6$

Cancel the common factors.

Factor $2$ out of $16$ .

$x = \frac{5}{8} + \frac{2 (5 y)}{2 (8)}$

$- 8 x - 6 y = 6$

Cancel the common factor.

$x = \frac{5}{8} + \frac{2 (5 y)}{2 \cdot 8}$

$- 8 x - 6 y = 6$

Rewrite the expression.

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 8 x - 6 y = 6$

Step 2

Replace all occurrences of $x$ with $\frac{5}{8} + \frac{5 y}{8}$ in each equation.

Replace all occurrences of $x$ in $- 8 x - 6 y = 6$ with $\frac{5}{8} + \frac{5 y}{8}$ .

$- 8 (\frac{5}{8} + \frac{5 y}{8}) - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Simplify the left side.

Simplify $- 8 (\frac{5}{8} + \frac{5 y}{8}) - 6 y$ .

Simplify each term.

Apply the distributive property.

$- 8 (\frac{5}{8}) - 8 \frac{5 y}{8} - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8$ .

$8 (- 1) (\frac{5}{8}) - 8 \frac{5 y}{8} - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Cancel the common factor.

$8 \cdot (- 1 (\frac{5}{8})) - 8 \frac{5 y}{8} - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Rewrite the expression.

$- 1 \cdot 5 - 8 \frac{5 y}{8} - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 1 \cdot 5 - 8 \frac{5 y}{8} - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Multiply $- 1$ by $5$ .

$- 5 - 8 \frac{5 y}{8} - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8$ .

$- 5 + 8 (- 1) (\frac{5 y}{8}) - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Cancel the common factor.

$- 5 + 8 \cdot (- 1 \frac{5 y}{8}) - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Rewrite the expression.

$- 5 - 1 (5 y) - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 5 - 1 (5 y) - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Multiply $5$ by $- 1$ .

$- 5 - 5 y - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 5 - 5 y - 6 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Subtract $6 y$ from $- 5 y$ .

$- 5 - 11 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 5 - 11 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 5 - 11 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 5 - 11 y = 6$

$x = \frac{5}{8} + \frac{5 y}{8}$

Step 3

Solve for $y$ in $- 5 - 11 y = 6$ .

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

Add $5$ to both sides of the equation.

$- 11 y = 6 + 5$

$x = \frac{5}{8} + \frac{5 y}{8}$

Add $6$ and $5$ .

$- 11 y = 11$

$x = \frac{5}{8} + \frac{5 y}{8}$

$- 11 y = 11$

$x = \frac{5}{8} + \frac{5 y}{8}$

Divide each term in $- 11 y = 11$ by $- 11$ and simplify.

Divide each term in $- 11 y = 11$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{11}{- 11}$

$x = \frac{5}{8} + \frac{5 y}{8}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{11}{- 11}$

$x = \frac{5}{8} + \frac{5 y}{8}$

Divide $y$ by $1$ .

$y = \frac{11}{- 11}$

$x = \frac{5}{8} + \frac{5 y}{8}$

$y = \frac{11}{- 11}$

$x = \frac{5}{8} + \frac{5 y}{8}$

$y = \frac{11}{- 11}$

$x = \frac{5}{8} + \frac{5 y}{8}$

Simplify the right side.

Divide $11$ by $- 11$ .

$y = - 1$

$x = \frac{5}{8} + \frac{5 y}{8}$

$y = - 1$

$x = \frac{5}{8} + \frac{5 y}{8}$

$y = - 1$

$x = \frac{5}{8} + \frac{5 y}{8}$

$y = - 1$

$x = \frac{5}{8} + \frac{5 y}{8}$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{5}{8} + \frac{5 y}{8}$ with $- 1$ .

$x = \frac{5}{8} + \frac{5 (- 1)}{8}$

$y = - 1$

Simplify the right side.

Simplify $\frac{5}{8} + \frac{5 (- 1)}{8}$ .

Combine the numerators over the common denominator.

$x = \frac{5 + 5 (- 1)}{8}$

$y = - 1$

Simplify the expression.

Multiply $5$ by $- 1$ .

$x = \frac{5 - 5}{8}$

$y = - 1$

Subtract $5$ from $5$ .

$x = \frac{0}{8}$

$y = - 1$

Divide $0$ by $8$ .

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

$x = 0$

$y = - 1$

Step 5

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

$(0, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 1)$

Equation Form:

$x = 0, y = - 1$

Step 7

Related Questions