Precalculus Examples

$y = 5 x - 2$ , $y = - 2 x + 5$

Step 1

Eliminate the equal sides of each equation and combine.

$5 x - 2 = - 2 x + 5$

Step 2

Solve $5 x - 2 = - 2 x + 5$ 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

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

$5 x - 2 + 2 x = 5$

Step 2.1.2

Add $5 x$ and $2 x$ .

$7 x - 2 = 5$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the equation.

$7 x = 5 + 2$

Step 2.2.2

Add $5$ and $2$ .

$7 x = 7$

Step 2.3

Divide each term in $7 x = 7$ by $7$ and simplify.

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Step 2.3.1

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{7}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $7$ by $7$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

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Step 3.1

Substitute $1$ for $x$ .

$y = - 2 \cdot 1 + 5$

Step 3.2

Substitute $1$ for $x$ in $y = - 2 \cdot 1 + 5$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = - 2 \cdot 1 + 5$

Step 3.2.2

Simplify $- 2 \cdot 1 + 5$ .

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Step 3.2.2.1

Multiply $- 2$ by $1$ .

$y = - 2 + 5$

Step 3.2.2.2

Add $- 2$ and $5$ .

$y = 3$

Step 4

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

$(1, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 6