Precalculus Examples

$x + y = 0$ , $x - y = 0$

Solve the system of equations.

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Add the two equations together to eliminate $y$ from the system.

Divide each term by $2$ and simplify.

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Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Divide $0$ by $2$ .

$x = 0$

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

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Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$(0) + y = 0$

Add $0$ and $y$ .

$y = 0$

The solution to the independent system of equations can be represented as a point.

$(0, 0)$

Since the system has a point of intersection, the system is independent.

Independent

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