Precalculus Examples

$x - 2 y = 3$ , $2 x = 4 y + 6$

Step 1

Add $2 y$ to both sides of the equation.

$x = 3 + 2 y$

$2 x = 4 y + 6$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $2 x = 4 y + 6$ with $3 + 2 y$ .

$2 (3 + 2 y) = 4 y + 6$

$x = 3 + 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (3 + 2 y)$ .

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Step 2.2.1.1

Apply the distributive property.

$2 \cdot 3 + 2 (2 y) = 4 y + 6$

$x = 3 + 2 y$

Step 2.2.1.2

Multiply.

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Step 2.2.1.2.1

Multiply $2$ by $3$ .

$6 + 2 (2 y) = 4 y + 6$

$x = 3 + 2 y$

Step 2.2.1.2.2

Multiply $2$ by $2$ .

$6 + 4 y = 4 y + 6$

$x = 3 + 2 y$

$6 + 4 y = 4 y + 6$

$x = 3 + 2 y$

$6 + 4 y = 4 y + 6$

$x = 3 + 2 y$

$6 + 4 y = 4 y + 6$

$x = 3 + 2 y$

$6 + 4 y = 4 y + 6$

$x = 3 + 2 y$

Step 3

Solve for $y$ in $6 + 4 y = 4 y + 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4 y$ from both sides of the equation.

$6 + 4 y - 4 y = 6$

$x = 3 + 2 y$

Step 3.1.2

Combine the opposite terms in $6 + 4 y - 4 y$ .

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Step 3.1.2.1

Subtract $4 y$ from $4 y$ .

$6 + 0 = 6$

$x = 3 + 2 y$

Step 3.1.2.2

Add $6$ and $0$ .

$6 = 6$

$x = 3 + 2 y$

$6 = 6$

$x = 3 + 2 y$

$6 = 6$

$x = 3 + 2 y$

Step 3.2

Since $6 = 6$ , the equation will always be true.

Always true

$x = 3 + 2 y$

Always true

$x = 3 + 2 y$

Step 4

Remove any equations from the system that are always true.

$x = 3 + 2 y$

Step 5