Algebra Examples

$4 x - y = 6$ $2 x - \frac{y}{2} = 4$

Step 1

Solve for $x$ in $4 x - y = 6$ .

Tap for more steps...

Step 1.1

Add $y$ to both sides of the equation.

$4 x = 6 + y$

$2 x - \frac{y}{2} = 4$

Step 1.2

Divide each term in $4 x = 6 + y$ by $4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $4 x = 6 + y$ by $4$ .

$\frac{4 x}{4} = \frac{6}{4} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{6}{4} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{4} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{6}{4} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{6}{4} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Cancel the common factor of $6$ and $4$ .

Tap for more steps...

Step 1.2.3.1.1

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{4} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 1.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 3}{2 \cdot 2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 1.2.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 1.2.3.1.2.3

Rewrite the expression.

$x = \frac{3}{2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$2 x - \frac{y}{2} = 4$

Step 2

Replace all occurrences of $x$ with $\frac{3}{2} + \frac{y}{4}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $2 x - \frac{y}{2} = 4$ with $\frac{3}{2} + \frac{y}{4}$ .

$2 (\frac{3}{2} + \frac{y}{4}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $2 (\frac{3}{2} + \frac{y}{4}) - \frac{y}{2}$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$2 (\frac{3}{2}) + 2 (\frac{y}{4}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

$2 (\frac{3}{2}) + 2 (\frac{y}{4}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.1.2.2

Rewrite the expression.

$3 + 2 (\frac{y}{4}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 + 2 (\frac{y}{4}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.3.1

Factor $2$ out of $4$ .

$3 + 2 (\frac{y}{2 (2)}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.1.3.2

Cancel the common factor.

$3 + 2 (\frac{y}{2 \cdot 2}) - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.1.3.3

Rewrite the expression.

$3 + \frac{y}{2} - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 + \frac{y}{2} - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 + \frac{y}{2} - \frac{y}{2} = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.2

Combine the opposite terms in $3 + \frac{y}{2} - \frac{y}{2}$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $\frac{y}{2}$ from $\frac{y}{2}$ .

$3 + 0 = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 2.2.1.2.2

Add $3$ and $0$ .

$3 = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 = 4$

$x = \frac{3}{2} + \frac{y}{4}$

$3 = 4$

$x = \frac{3}{2} + \frac{y}{4}$

Step 3

Since $3 = 4$ is not true, there is no solution.

No solution

Step 4