Solve the System of Equations y=x-4 x+2y=16

$y = x - 4$ $x + 2 y = 16$

Step 1

Replace all occurrences of $y$ with $x - 4$ in each equation.

Replace all occurrences of $y$ in $x + 2 y = 16$ with $x - 4$ .

$x + 2 (x - 4) = 16$

$y = x - 4$

Simplify the left side.

Simplify $x + 2 (x - 4)$ .

Simplify each term.

Apply the distributive property.

$x + 2 x + 2 \cdot - 4 = 16$

$y = x - 4$

Multiply $2$ by $- 4$ .

$x + 2 x - 8 = 16$

$y = x - 4$

$x + 2 x - 8 = 16$

$y = x - 4$

Add $x$ and $2 x$ .

$3 x - 8 = 16$

$y = x - 4$

$3 x - 8 = 16$

$y = x - 4$

$3 x - 8 = 16$

$y = x - 4$

$3 x - 8 = 16$

$y = x - 4$

Step 2

Solve for $x$ in $3 x - 8 = 16$ .

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

Add $8$ to both sides of the equation.

$3 x = 16 + 8$

$y = x - 4$

Add $16$ and $8$ .

$3 x = 24$

$y = x - 4$

$3 x = 24$

$y = x - 4$

Divide each term in $3 x = 24$ by $3$ and simplify.

Divide each term in $3 x = 24$ by $3$ .

$\frac{3 x}{3} = \frac{24}{3}$

$y = x - 4$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{24}{3}$

$y = x - 4$

Divide $x$ by $1$ .

$x = \frac{24}{3}$

$y = x - 4$

$x = \frac{24}{3}$

$y = x - 4$

$x = \frac{24}{3}$

$y = x - 4$

Simplify the right side.

Divide $24$ by $3$ .

$x = 8$

$y = x - 4$

$x = 8$

$y = x - 4$

$x = 8$

$y = x - 4$

$x = 8$

$y = x - 4$

Step 3

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

Replace all occurrences of $x$ in $y = x - 4$ with $8$ .

$y = (8) - 4$

$x = 8$

Simplify the right side.

Subtract $4$ from $8$ .

$y = 4$

$x = 8$

$y = 4$

$x = 8$

$y = 4$

$x = 8$

Step 4

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

$(8, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(8, 4)$

Equation Form:

$x = 8, y = 4$

Step 6

Solve the System of Equations y=x-4 x+2y=16

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