Finite Math Examples

$- x + y = 3$ , $2 x + y = 6$

Step 1

Add $x$ to both sides of the equation.

$y = 3 + x$

$2 x + y = 6$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $2 x + y = 6$ with $3 + x$ .

$2 x + 3 + x = 6$

$y = 3 + x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 x + 3 + x$ .

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Step 2.2.1.1

Remove parentheses.

$2 x + 3 + x = 6$

$y = 3 + x$

Step 2.2.1.2

Add $2 x$ and $x$ .

$3 x + 3 = 6$

$y = 3 + x$

$3 x + 3 = 6$

$y = 3 + x$

$3 x + 3 = 6$

$y = 3 + x$

$3 x + 3 = 6$

$y = 3 + x$

Step 3

Solve for $x$ in $3 x + 3 = 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $3$ from both sides of the equation.

$3 x = 6 - 3$

$y = 3 + x$

Step 3.1.2

Subtract $3$ from $6$ .

$3 x = 3$

$y = 3 + x$

$3 x = 3$

$y = 3 + x$

Step 3.2

Divide each term in $3 x = 3$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

$y = 3 + x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

$y = 3 + x$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{3}$

$y = 3 + x$

$x = \frac{3}{3}$

$y = 3 + x$

$x = \frac{3}{3}$

$y = 3 + x$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $3$ by $3$ .

$x = 1$

$y = 3 + x$

$x = 1$

$y = 3 + x$

$x = 1$

$y = 3 + x$

$x = 1$

$y = 3 + x$

Step 4

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

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Step 4.1

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

$y = 3 + 1$

$x = 1$

Step 4.2

Simplify $y = 3 + 1$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$y = 3 + 1$

$x = 1$

$y = 3 + 1$

$x = 1$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $3$ and $1$ .

$y = 4$

$x = 1$

$y = 4$

$x = 1$

$y = 4$

$x = 1$

$y = 4$

$x = 1$

Step 5

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

$(1, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 4)$

Equation Form:

$x = 1, y = 4$

Step 7