Solve the System of Equations x+2y=22 and 4x+y=46

$x + 2 y = 22$ and $4 x + y = 46$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 22 - 2 y$

$4 x + y = 46$

Step 2

Replace all occurrences of $x$ with $22 - 2 y$ in each equation.

Replace all occurrences of $x$ in $4 x + y = 46$ with $22 - 2 y$ .

$4 (22 - 2 y) + y = 46$

$x = 22 - 2 y$

Simplify the left side.

Simplify $4 (22 - 2 y) + y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 22 + 4 (- 2 y) + y = 46$

$x = 22 - 2 y$

Multiply $4$ by $22$ .

$88 + 4 (- 2 y) + y = 46$

$x = 22 - 2 y$

Multiply $- 2$ by $4$ .

$88 - 8 y + y = 46$

$x = 22 - 2 y$

$88 - 8 y + y = 46$

$x = 22 - 2 y$

Add $- 8 y$ and $y$ .

$88 - 7 y = 46$

$x = 22 - 2 y$

$88 - 7 y = 46$

$x = 22 - 2 y$

$88 - 7 y = 46$

$x = 22 - 2 y$

$88 - 7 y = 46$

$x = 22 - 2 y$

Step 3

Solve for $y$ in $88 - 7 y = 46$ .

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

Subtract $88$ from both sides of the equation.

$- 7 y = 46 - 88$

$x = 22 - 2 y$

Subtract $88$ from $46$ .

$- 7 y = - 42$

$x = 22 - 2 y$

$- 7 y = - 42$

$x = 22 - 2 y$

Divide each term in $- 7 y = - 42$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 42$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 42}{- 7}$

$x = 22 - 2 y$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 42}{- 7}$

$x = 22 - 2 y$

Divide $y$ by $1$ .

$y = \frac{- 42}{- 7}$

$x = 22 - 2 y$

$y = \frac{- 42}{- 7}$

$x = 22 - 2 y$

$y = \frac{- 42}{- 7}$

$x = 22 - 2 y$

Simplify the right side.

Divide $- 42$ by $- 7$ .

$y = 6$

$x = 22 - 2 y$

$y = 6$

$x = 22 - 2 y$

$y = 6$

$x = 22 - 2 y$

$y = 6$

$x = 22 - 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = 22 - 2 y$ with $6$ .

$x = 22 - 2 \cdot 6$

$y = 6$

Simplify the right side.

Simplify $22 - 2 \cdot 6$ .

Multiply $- 2$ by $6$ .

$x = 22 - 12$

$y = 6$

Subtract $12$ from $22$ .

$x = 10$

$y = 6$

$x = 10$

$y = 6$

$x = 10$

$y = 6$

$x = 10$

$y = 6$

Step 5

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

$(10, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(10, 6)$

Equation Form:

$x = 10, y = 6$

Step 7

Solve the System of Equations x+2y=22 and 4x+y=46

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