Algebra Examples

$2 y = 5 x + 4$ $y = 3 x + 2$

Step 1

Replace all occurrences of $y$ with $3 x + 2$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $2 y = 5 x + 4$ with $3 x + 2$ .

$2 (3 x + 2) = 5 x + 4$

$y = 3 x + 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 (3 x + 2)$ .

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Step 1.2.1.1

Apply the distributive property.

$2 (3 x) + 2 \cdot 2 = 5 x + 4$

$y = 3 x + 2$

Step 1.2.1.2

Multiply.

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Step 1.2.1.2.1

Multiply $3$ by $2$ .

$6 x + 2 \cdot 2 = 5 x + 4$

$y = 3 x + 2$

Step 1.2.1.2.2

Multiply $2$ by $2$ .

$6 x + 4 = 5 x + 4$

$y = 3 x + 2$

$6 x + 4 = 5 x + 4$

$y = 3 x + 2$

$6 x + 4 = 5 x + 4$

$y = 3 x + 2$

$6 x + 4 = 5 x + 4$

$y = 3 x + 2$

$6 x + 4 = 5 x + 4$

$y = 3 x + 2$

Step 2

Solve for $x$ in $6 x + 4 = 5 x + 4$ .

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Step 2.1

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

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Step 2.1.1

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

$6 x + 4 - 5 x = 4$

$y = 3 x + 2$

Step 2.1.2

Subtract $5 x$ from $6 x$ .

$x + 4 = 4$

$y = 3 x + 2$

$x + 4 = 4$

$y = 3 x + 2$

Step 2.2

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

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Step 2.2.1

Subtract $4$ from both sides of the equation.

$x = 4 - 4$

$y = 3 x + 2$

Step 2.2.2

Subtract $4$ from $4$ .

$x = 0$

$y = 3 x + 2$

$x = 0$

$y = 3 x + 2$

$x = 0$

$y = 3 x + 2$

Step 3

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

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Step 3.1

Replace all occurrences of $x$ in $y = 3 x + 2$ with $0$ .

$y = 3 (0) + 2$

$x = 0$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $3 (0) + 2$ .

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Step 3.2.1.1

Multiply $3$ by $0$ .

$y = 0 + 2$

$x = 0$

Step 3.2.1.2

Add $0$ and $2$ .

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

Step 4

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

$(0, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 2)$

Equation Form:

$x = 0, y = 2$

Step 6