Algebra Examples

$z = 3 y + 4$ and $z = - y$

Step 1

Eliminate the equal sides of each equation and combine.

$3 y + 4 = - y$

Step 2

Solve $3 y + 4 = - y$ for $y$ .

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Step 2.1

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

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Step 2.1.1

Add $y$ to both sides of the equation.

$3 y + 4 + y = 0$

Step 2.1.2

Add $3 y$ and $y$ .

$4 y + 4 = 0$

Step 2.2

Subtract $4$ from both sides of the equation.

$4 y = - 4$

Step 2.3

Divide each term in $4 y = - 4$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 y = - 4$ by $4$ .

$\frac{4 y}{4} = \frac{- 4}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 4}{4}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 4$ by $4$ .

$y = - 1$

Step 3

Evaluate $z$ when $y = - 1$ .

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Step 3.1

Substitute $- 1$ for $y$ .

$z = - (- 1)$

Step 3.2

Multiply $- 1$ by $- 1$ .

$z = 1$

Step 4

The solution of the system of equations is all the values that make the system true.

$z = 1, y = - 1$