Algebra Examples

$3 x - 2 y = 0$ $x - y = - 1$

Step 1

Add $y$ to both sides of the equation.

$x = - 1 + y$

$3 x - 2 y = 0$

Step 2

Replace all occurrences of $x$ with $- 1 + y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x - 2 y = 0$ with $- 1 + y$ .

$3 (- 1 + y) - 2 y = 0$

$x = - 1 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (- 1 + y) - 2 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$3 \cdot - 1 + 3 y - 2 y = 0$

$x = - 1 + y$

Step 2.2.1.1.2

Multiply $3$ by $- 1$ .

$- 3 + 3 y - 2 y = 0$

$x = - 1 + y$

$- 3 + 3 y - 2 y = 0$

$x = - 1 + y$

Step 2.2.1.2

Subtract $2 y$ from $3 y$ .

$- 3 + y = 0$

$x = - 1 + y$

$- 3 + y = 0$

$x = - 1 + y$

$- 3 + y = 0$

$x = - 1 + y$

$- 3 + y = 0$

$x = - 1 + y$

Step 3

Add $3$ to both sides of the equation.

$y = 3$

$x = - 1 + y$

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 1 + y$ with $3$ .

$x = - 1 + 3$

$y = 3$

Step 4.2

Simplify $x = - 1 + 3$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 1 + 3$

$y = 3$

$x = - 1 + 3$

$y = 3$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $- 1$ and $3$ .

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

Step 5

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

$(2, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 7