Algebra Examples

$4 y + 3 = 3 y + x$ $2 x + 4 y = 18$

Step 1

Solve for $y$ in $4 y + 3 = 3 y + x$ .

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Step 1.1

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

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Step 1.1.1

Subtract $3 y$ from both sides of the equation.

$4 y + 3 - 3 y = x$

$2 x + 4 y = 18$

Step 1.1.2

Subtract $3 y$ from $4 y$ .

$y + 3 = x$

$2 x + 4 y = 18$

$y + 3 = x$

$2 x + 4 y = 18$

Step 1.2

Subtract $3$ from both sides of the equation.

$y = x - 3$

$2 x + 4 y = 18$

$y = x - 3$

$2 x + 4 y = 18$

Step 2

Replace all occurrences of $y$ with $x - 3$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $2 x + 4 y = 18$ with $x - 3$ .

$2 x + 4 (x - 3) = 18$

$y = x - 3$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 x + 4 (x - 3)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$2 x + 4 x + 4 \cdot - 3 = 18$

$y = x - 3$

Step 2.2.1.1.2

Multiply $4$ by $- 3$ .

$2 x + 4 x - 12 = 18$

$y = x - 3$

$2 x + 4 x - 12 = 18$

$y = x - 3$

Step 2.2.1.2

Add $2 x$ and $4 x$ .

$6 x - 12 = 18$

$y = x - 3$

$6 x - 12 = 18$

$y = x - 3$

$6 x - 12 = 18$

$y = x - 3$

$6 x - 12 = 18$

$y = x - 3$

Step 3

Solve for $x$ in $6 x - 12 = 18$ .

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Step 3.1

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

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Step 3.1.1

Add $12$ to both sides of the equation.

$6 x = 18 + 12$

$y = x - 3$

Step 3.1.2

Add $18$ and $12$ .

$6 x = 30$

$y = x - 3$

$6 x = 30$

$y = x - 3$

Step 3.2

Divide each term in $6 x = 30$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 x = 30$ by $6$ .

$\frac{6 x}{6} = \frac{30}{6}$

$y = x - 3$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{30}{6}$

$y = x - 3$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{6}$

$y = x - 3$

$x = \frac{30}{6}$

$y = x - 3$

$x = \frac{30}{6}$

$y = x - 3$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $30$ by $6$ .

$x = 5$

$y = x - 3$

$x = 5$

$y = x - 3$

$x = 5$

$y = x - 3$

$x = 5$

$y = x - 3$

Step 4

Replace all occurrences of $x$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = x - 3$ with $5$ .

$y = (5) - 3$

$x = 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Subtract $3$ from $5$ .

$y = 2$

$x = 5$

$y = 2$

$x = 5$

$y = 2$

$x = 5$

Step 5

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

$(5, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 2)$

Equation Form:

$x = 5, y = 2$

Step 7