Algebra Examples

$y = \frac{5}{2} x + 2$ $2 y = 5 x + 8$

Step 1

Combine $\frac{5}{2}$ and $x$ .

$y = \frac{5 x}{2} + 2$

$2 y = 5 x + 8$

Step 2

Replace all occurrences of $y$ with $\frac{5 x}{2} + 2$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $2 y = 5 x + 8$ with $\frac{5 x}{2} + 2$ .

$2 (\frac{5 x}{2} + 2) = 5 x + 8$

$y = \frac{5 x}{2} + 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (\frac{5 x}{2} + 2)$ .

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Step 2.2.1.1

Apply the distributive property.

$2 (\frac{5 x}{2}) + 2 \cdot 2 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Cancel the common factor.

$2 (\frac{5 x}{2}) + 2 \cdot 2 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

Step 2.2.1.2.2

Rewrite the expression.

$5 x + 2 \cdot 2 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

$5 x + 2 \cdot 2 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

Step 2.2.1.3

Multiply $2$ by $2$ .

$5 x + 4 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

$5 x + 4 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

$5 x + 4 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

$5 x + 4 = 5 x + 8$

$y = \frac{5 x}{2} + 2$

Step 3

Solve for $x$ in $5 x + 4 = 5 x + 8$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5 x$ from both sides of the equation.

$5 x + 4 - 5 x = 8$

$y = \frac{5 x}{2} + 2$

Step 3.1.2

Combine the opposite terms in $5 x + 4 - 5 x$ .

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Step 3.1.2.1

Subtract $5 x$ from $5 x$ .

$0 + 4 = 8$

$y = \frac{5 x}{2} + 2$

Step 3.1.2.2

Add $0$ and $4$ .

$4 = 8$

$y = \frac{5 x}{2} + 2$

$4 = 8$

$y = \frac{5 x}{2} + 2$

$4 = 8$

$y = \frac{5 x}{2} + 2$

Step 3.2

Since $4 \neq 8$ , there are no solutions.

No solution

$y = \frac{5 x}{2} + 2$

No solution

Step 4