Algebra Examples

$y = \frac{3}{4} x + 1$ $y = \frac{1}{4} x + 3$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{3}{4} x + 1 = \frac{1}{4} x + 3$

Step 2

Solve $\frac{3}{4} x + 1 = \frac{1}{4} x + 3$ for $x$ .

Tap for more steps...

Step 2.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + 1 = \frac{1}{4} x + 3$

Step 2.2

Combine $\frac{1}{4}$ and $x$ .

$\frac{3 x}{4} + 1 = \frac{x}{4} + 3$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Subtract $\frac{x}{4}$ from both sides of the equation.

$\frac{3 x}{4} + 1 - \frac{x}{4} = 3$

Step 2.3.2

Combine the numerators over the common denominator.

$1 + \frac{3 x - x}{4} = 3$

Step 2.3.3

Subtract $x$ from $3 x$ .

$1 + \frac{2 x}{4} = 3$

Step 2.3.4

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 2.3.4.1

Factor $2$ out of $2 x$ .

$1 + \frac{2 (x)}{4} = 3$

Step 2.3.4.2

Cancel the common factors.

Tap for more steps...

Step 2.3.4.2.1

Factor $2$ out of $4$ .

$1 + \frac{2 x}{2 \cdot 2} = 3$

Step 2.3.4.2.2

Cancel the common factor.

$1 + \frac{2 x}{2 \cdot 2} = 3$

Step 2.3.4.2.3

Rewrite the expression.

$1 + \frac{x}{2} = 3$

Step 2.4

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

Tap for more steps...

Step 2.4.1

Subtract $1$ from both sides of the equation.

$\frac{x}{2} = 3 - 1$

Step 2.4.2

Subtract $1$ from $3$ .

$\frac{x}{2} = 2$

Step 2.5

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 2$

Step 2.6

Simplify both sides of the equation.

Tap for more steps...

Step 2.6.1

Simplify the left side.

Tap for more steps...

Step 2.6.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.6.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 2$

Step 2.6.1.1.2

Rewrite the expression.

$x = 2 \cdot 2$

Step 2.6.2

Simplify the right side.

Tap for more steps...

Step 2.6.2.1

Multiply $2$ by $2$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Tap for more steps...

Step 3.1

Substitute $4$ for $x$ .

$y = \frac{1}{4} \cdot (4) + 3$

Step 3.2

Substitute $4$ for $x$ in $y = \frac{1}{4} \cdot (4) + 3$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Multiply $\frac{1}{4}$ by $4$ .

$y = \frac{1}{4} \cdot 4 + 3$

Step 3.2.2

Simplify $\frac{1}{4} \cdot 4 + 3$ .

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$y = \frac{1}{4} \cdot 4 + 3$

Step 3.2.2.1.2

Rewrite the expression.

$y = 1 + 3$

Step 3.2.2.2

Add $1$ and $3$ .

$y = 4$

Step 4

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

$(4, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 4)$

Equation Form:

$x = 4, y = 4$

Step 6