Finite Math Examples

$- x + y = 4$ , $2 x - y = - 1$

Step 1

Add $x$ to both sides of the equation.

$y = 4 + x$

$2 x - y = - 1$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $2 x - y = - 1$ with $4 + x$ .

$2 x - (4 + x) = - 1$

$y = 4 + x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 x - (4 + x)$ .

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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.

$2 x - 1 \cdot 4 - x = - 1$

$y = 4 + x$

Step 2.2.1.1.2

Multiply $- 1$ by $4$ .

$2 x - 4 - x = - 1$

$y = 4 + x$

$2 x - 4 - x = - 1$

$y = 4 + x$

Step 2.2.1.2

Subtract $x$ from $2 x$ .

$x - 4 = - 1$

$y = 4 + x$

$x - 4 = - 1$

$y = 4 + x$

$x - 4 = - 1$

$y = 4 + x$

$x - 4 = - 1$

$y = 4 + x$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$x = - 1 + 4$

$y = 4 + x$

Step 3.2

Add $- 1$ and $4$ .

$x = 3$

$y = 4 + x$

$x = 3$

$y = 4 + x$

Step 4

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

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Step 4.1

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

$y = 4 + 3$

$x = 3$

Step 4.2

Simplify $y = 4 + 3$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$y = 4 + 3$

$x = 3$

$y = 4 + 3$

$x = 3$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $4$ and $3$ .

$y = 7$

$x = 3$

$y = 7$

$x = 3$

$y = 7$

$x = 3$

$y = 7$

$x = 3$

Step 5

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

$(3, 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 7)$

Equation Form:

$x = 3, y = 7$

Step 7