Pre-Algebra Examples

$y = 4 x$ , $x = 2 y$

Step 1

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

Tap for more steps...

Step 1.1

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

$x = 2 (4 x)$

$y = 4 x$

Step 1.2

Simplify the right side.

Tap for more steps...

Step 1.2.1

Multiply $4$ by $2$ .

$x = 8 x$

$y = 4 x$

$x = 8 x$

$y = 4 x$

$x = 8 x$

$y = 4 x$

Step 2

Solve for $x$ in $x = 8 x$ .

Tap for more steps...

Step 2.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.1.1

Subtract $8 x$ from both sides of the equation.

$x - 8 x = 0$

$y = 4 x$

Step 2.1.2

Subtract $8 x$ from $x$ .

$- 7 x = 0$

$y = 4 x$

$- 7 x = 0$

$y = 4 x$

Step 2.2

Divide each term in $- 7 x = 0$ by $- 7$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- 7 x = 0$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{0}{- 7}$

$y = 4 x$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $- 7$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{0}{- 7}$

$y = 4 x$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 7}$

$y = 4 x$

$x = \frac{0}{- 7}$

$y = 4 x$

$x = \frac{0}{- 7}$

$y = 4 x$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $0$ by $- 7$ .

$x = 0$

$y = 4 x$

$x = 0$

$y = 4 x$

$x = 0$

$y = 4 x$

$x = 0$

$y = 4 x$

Step 3

Replace all occurrences of $x$ with $0$ in each equation.

Tap for more steps...

Step 3.1

Replace all occurrences of $x$ in $y = 4 x$ with $0$ .

$y = 4 (0)$

$x = 0$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $4$ by $0$ .

$y = 0$

$x = 0$

$y = 0$

$x = 0$

$y = 0$

$x = 0$

Step 4

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

$(0, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 0)$

Equation Form:

$x = 0, y = 0$

Step 6