Algebra Examples

$y = - x + 3$ and $y = x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$- x + 3 = x - 1$

Step 2

Solve $- x + 3 = x - 1$ for $x$ .

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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 $x$ from both sides of the equation.

$- x + 3 - x = - 1$

Step 2.1.2

Subtract $x$ from $- x$ .

$- 2 x + 3 = - 1$

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 $3$ from both sides of the equation.

$- 2 x = - 1 - 3$

Step 2.2.2

Subtract $3$ from $- 1$ .

$- 2 x = - 4$

Step 2.3

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

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Step 2.3.1

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 4$ by $- 2$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

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Step 3.1

Substitute $2$ for $x$ .

$y = (2) - 1$

Step 3.2

Substitute $2$ for $x$ in $y = (2) - 1$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = 2 - 1$

Step 3.2.2

Remove parentheses.

$y = (2) - 1$

Step 3.2.3

Subtract $1$ from $2$ .

$y = 1$

Step 4

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

$(2, 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 6