Precalculus Examples

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

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 4 - 2 x$

$x - y = 2$

Step 2

Subtract $x$ from both sides of the equation.

$- y = 2 - x$

$y = 4 - 2 x$

Step 3

Divide each term in $- y = 2 - x$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = 2 - x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2}{- 1} + \frac{- x}{- 1}$

$y = 4 - 2 x$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2}{- 1} + \frac{- x}{- 1}$

$y = 4 - 2 x$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{2}{- 1} + \frac{- x}{- 1}$

$y = 4 - 2 x$

$y = \frac{2}{- 1} + \frac{- x}{- 1}$

$y = 4 - 2 x$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $2$ by $- 1$ .

$y = - 2 + \frac{- x}{- 1}$

$y = 4 - 2 x$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$y = - 2 + \frac{x}{1}$

$y = 4 - 2 x$

Step 3.3.1.3

Divide $x$ by $1$ .

$y = - 2 + x$

$y = 4 - 2 x$

$y = - 2 + x$

$y = 4 - 2 x$

$y = - 2 + x$

$y = 4 - 2 x$

$y = - 2 + x$

$y = 4 - 2 x$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(2, 0)$

Step 5