Finite Math Examples

$x = y - 3$ , $2 x - y = 7$

Step 1

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

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Step 1.1

Replace all occurrences of $x$ in $2 x - y = 7$ with $y - 3$ .

$2 (y - 3) - y = 7$

$x = y - 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$2 y + 2 \cdot - 3 - y = 7$

$x = y - 3$

Step 1.2.1.1.2

Multiply $2$ by $- 3$ .

$2 y - 6 - y = 7$

$x = y - 3$

$2 y - 6 - y = 7$

$x = y - 3$

Step 1.2.1.2

Subtract $y$ from $2 y$ .

$y - 6 = 7$

$x = y - 3$

$y - 6 = 7$

$x = y - 3$

$y - 6 = 7$

$x = y - 3$

$y - 6 = 7$

$x = y - 3$

Step 2

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

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Step 2.1

Add $6$ to both sides of the equation.

$y = 7 + 6$

$x = y - 3$

Step 2.2

Add $7$ and $6$ .

$y = 13$

$x = y - 3$

$y = 13$

$x = y - 3$

Step 3

Replace all occurrences of $y$ with $13$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $x = y - 3$ with $13$ .

$x = (13) - 3$

$y = 13$

Step 3.2

Simplify the right side.

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Step 3.2.1

Subtract $3$ from $13$ .

$x = 10$

$y = 13$

$x = 10$

$y = 13$

$x = 10$

$y = 13$

Step 4

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

$(10, 13)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(10, 13)$

Equation Form:

$x = 10, y = 13$

Step 6