Finite Math Examples

$2 x + y = 6$ , $x + y = 4$ , $x = 1$ , $x = 0$

Step 1

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

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Step 1.1

Replace all occurrences of $x$ in $2 x + y = 6$ with $1$ .

$2 (1) + y = 6$

$x = 1$

$x + y = 4$

$x = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $2$ by $1$ .

$2 + y = 6$

$x = 1$

$x + y = 4$

$x = 0$

$2 + y = 6$

$x = 1$

$x + y = 4$

$x = 0$

Step 1.3

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

$(1) + y = 4$

$2 + y = 6$

$x = 1$

$x = 0$

Step 1.4

Simplify the left side.

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Step 1.4.1

Remove parentheses.

$1 + y = 4$

$2 + y = 6$

$x = 1$

$x = 0$

$1 + y = 4$

$2 + y = 6$

$x = 1$

$x = 0$

$1 + y = 4$

$2 + y = 6$

$x = 1$

$x = 0$

Step 2

Replace all occurrences of $x$ with $0$ in each equation.

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Step 2.1

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

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Step 2.1.1

Subtract $1$ from both sides of the equation.

$y = 4 - 1$

$2 + y = 6$

$x = 1$

$x = 0$

Step 2.1.2

Subtract $1$ from $4$ .

$y = 3$

$2 + y = 6$

$x = 1$

$x = 0$

$y = 3$

$2 + y = 6$

$x = 1$

$x = 0$

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$y = 6 - 2$

$y = 3$

$x = 1$

$x = 0$

Step 2.2.2

Subtract $2$ from $6$ .

$y = 4$

$y = 3$

$x = 1$

$x = 0$

$y = 4$

$y = 3$

$x = 1$

$x = 0$

$y = 4$

$y = 3$

$x = 1$

$x = 0$

Step 3

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

$(1, 3)$

Step 4

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 5