Precalculus Examples

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

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 $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Divide $6$ by $2$ .

$x = 3$

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 $y$ .

$(3) + y = 4$

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

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Subtract $3$ from both sides of the equation.

$y = 4 - 3$

Subtract $3$ from $4$ .

$y = 1$

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

$(3, 1)$

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

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