Solve by Substitution x-2y=8 and 8x+6y=42

$x - 2 y = 8$ and $8 x + 6 y = 42$

Step 1

Add $2 y$ to both sides of the equation.

$x = 8 + 2 y$

$8 x + 6 y = 42$

Step 2

Replace all occurrences of $x$ with $8 + 2 y$ in each equation.

Replace all occurrences of $x$ in $8 x + 6 y = 42$ with $8 + 2 y$ .

$8 (8 + 2 y) + 6 y = 42$

$x = 8 + 2 y$

Simplify the left side.

Simplify $8 (8 + 2 y) + 6 y$ .

Simplify each term.

Apply the distributive property.

$8 \cdot 8 + 8 (2 y) + 6 y = 42$

$x = 8 + 2 y$

Multiply $8$ by $8$ .

$64 + 8 (2 y) + 6 y = 42$

$x = 8 + 2 y$

Multiply $2$ by $8$ .

$64 + 16 y + 6 y = 42$

$x = 8 + 2 y$

$64 + 16 y + 6 y = 42$

$x = 8 + 2 y$

Add $16 y$ and $6 y$ .

$64 + 22 y = 42$

$x = 8 + 2 y$

$64 + 22 y = 42$

$x = 8 + 2 y$

$64 + 22 y = 42$

$x = 8 + 2 y$

$64 + 22 y = 42$

$x = 8 + 2 y$

Step 3

Solve for $y$ in $64 + 22 y = 42$ .

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

Subtract $64$ from both sides of the equation.

$22 y = 42 - 64$

$x = 8 + 2 y$

Subtract $64$ from $42$ .

$22 y = - 22$

$x = 8 + 2 y$

$22 y = - 22$

$x = 8 + 2 y$

Divide each term in $22 y = - 22$ by $22$ and simplify.

Divide each term in $22 y = - 22$ by $22$ .

$\frac{22 y}{22} = \frac{- 22}{22}$

$x = 8 + 2 y$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 y}{22} = \frac{- 22}{22}$

$x = 8 + 2 y$

Divide $y$ by $1$ .

$y = \frac{- 22}{22}$

$x = 8 + 2 y$

$y = \frac{- 22}{22}$

$x = 8 + 2 y$

$y = \frac{- 22}{22}$

$x = 8 + 2 y$

Simplify the right side.

Divide $- 22$ by $22$ .

$y = - 1$

$x = 8 + 2 y$

$y = - 1$

$x = 8 + 2 y$

$y = - 1$

$x = 8 + 2 y$

$y = - 1$

$x = 8 + 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = 8 + 2 y$ with $- 1$ .

$x = 8 + 2 (- 1)$

$y = - 1$

Simplify the right side.

Simplify $8 + 2 (- 1)$ .

Multiply $2$ by $- 1$ .

$x = 8 - 2$

$y = - 1$

Subtract $2$ from $8$ .

$x = 6$

$y = - 1$

$x = 6$

$y = - 1$

$x = 6$

$y = - 1$

$x = 6$

$y = - 1$

Step 5

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

$(6, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, - 1)$

Equation Form:

$x = 6, y = - 1$

Step 7

Solve by Substitution x-2y=8 and 8x+6y=42

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