Finite Math Examples

$x + 4 y = 7$ , $\frac{1}{2} x + 2 = 5$

Step 1

Solve for $x$ in $\frac{1}{2} x + 2 = 5$ .

Tap for more steps...

Step 1.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + 2 = 5$

$x + 4 y = 7$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Subtract $2$ from both sides of the equation.

$\frac{x}{2} = 5 - 2$

$x + 4 y = 7$

Step 1.2.2

Subtract $2$ from $5$ .

$\frac{x}{2} = 3$

$x + 4 y = 7$

$\frac{x}{2} = 3$

$x + 4 y = 7$

Step 1.3

Multiply both sides of the equation by $2$ .

$2 (\frac{x}{2}) = 2 \cdot 3$

$x + 4 y = 7$

Step 1.4

Simplify both sides of the equation.

Tap for more steps...

Step 1.4.1

Simplify the left side.

Tap for more steps...

Step 1.4.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.4.1.1.1

Cancel the common factor.

$2 (\frac{x}{2}) = 2 \cdot 3$

$x + 4 y = 7$

Step 1.4.1.1.2

Rewrite the expression.

$x = 2 \cdot 3$

$x + 4 y = 7$

$x = 2 \cdot 3$

$x + 4 y = 7$

$x = 2 \cdot 3$

$x + 4 y = 7$

Step 1.4.2

Simplify the right side.

Tap for more steps...

Step 1.4.2.1

Multiply $2$ by $3$ .

$x = 6$

$x + 4 y = 7$

$x = 6$

$x + 4 y = 7$

$x = 6$

$x + 4 y = 7$

$x = 6$

$x + 4 y = 7$

Step 2

Replace all occurrences of $x$ with $6$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $x + 4 y = 7$ with $6$ .

$(6) + 4 y = 7$

$x = 6$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$6 + 4 y = 7$

$x = 6$

$6 + 4 y = 7$

$x = 6$

$6 + 4 y = 7$

$x = 6$

Step 3

Solve for $y$ in $6 + 4 y = 7$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $6$ from both sides of the equation.

$4 y = 7 - 6$

$x = 6$

Step 3.1.2

Subtract $6$ from $7$ .

$4 y = 1$

$x = 6$

$4 y = 1$

$x = 6$

Step 3.2

Divide each term in $4 y = 1$ by $4$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $4 y = 1$ by $4$ .

$\frac{4 y}{4} = \frac{1}{4}$

$x = 6$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{1}{4}$

$x = 6$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{4}$

$x = 6$

$y = \frac{1}{4}$

$x = 6$

$y = \frac{1}{4}$

$x = 6$

$y = \frac{1}{4}$

$x = 6$

$y = \frac{1}{4}$

$x = 6$

Step 4

Solve the system of equations.

$y = \frac{1}{4} x = 6$

Step 5

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

$(6, \frac{1}{4})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, \frac{1}{4})$

Equation Form:

$x = 6, y = \frac{1}{4}$

Step 7