Finite Math Examples

$3 x + 4 = - y$ , $2 x + y = 0$

Step 1

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

$y = - 2 x$

$3 x + 4 = - y$

Step 2

Replace all occurrences of $y$ with $- 2 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 x + 4 = - y$ with $- 2 x$ .

$3 x + 4 = - (- 2 x)$

$y = - 2 x$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 2$ by $- 1$ .

$3 x + 4 = 2 x$

$y = - 2 x$

$3 x + 4 = 2 x$

$y = - 2 x$

$3 x + 4 = 2 x$

$y = - 2 x$

Step 3

Solve for $x$ in $3 x + 4 = 2 x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

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

$3 x + 4 - 2 x = 0$

$y = - 2 x$

Step 3.1.2

Subtract $2 x$ from $3 x$ .

$x + 4 = 0$

$y = - 2 x$

$x + 4 = 0$

$y = - 2 x$

Step 3.2

Subtract $4$ from both sides of the equation.

$x = - 4$

$y = - 2 x$

$x = - 4$

$y = - 2 x$

Step 4

Replace all occurrences of $x$ with $- 4$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = - 2 x$ with $- 4$ .

$y = - 2 \cdot - 4$

$x = - 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 2$ by $- 4$ .

$y = 8$

$x = - 4$

$y = 8$

$x = - 4$

$y = 8$

$x = - 4$

Step 5

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

$(- 4, 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 8)$

Equation Form:

$x = - 4, y = 8$

Step 7