Finite Math Examples

$3 x + 4 y = 16$ , $- 5 y + y = 27$

Step 1

Divide each term in $- 4 y = 27$ by $- 4$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $- 4 y = 27$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{27}{- 4}$

$3 x + 4 y = 16$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{27}{- 4}$

$3 x + 4 y = 16$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{27}{- 4}$

$3 x + 4 y = 16$

$y = \frac{27}{- 4}$

$3 x + 4 y = 16$

$y = \frac{27}{- 4}$

$3 x + 4 y = 16$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Move the negative in front of the fraction.

$y = - \frac{27}{4}$

$3 x + 4 y = 16$

$y = - \frac{27}{4}$

$3 x + 4 y = 16$

$y = - \frac{27}{4}$

$3 x + 4 y = 16$

Step 2

Replace all occurrences of $y$ with $- \frac{27}{4}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $3 x + 4 y = 16$ with $- \frac{27}{4}$ .

$3 x + 4 (- \frac{27}{4}) = 16$

$y = - \frac{27}{4}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.1.1

Move the leading negative in $- \frac{27}{4}$ into the numerator.

$3 x + 4 (\frac{- 27}{4}) = 16$

$y = - \frac{27}{4}$

Step 2.2.1.2

Cancel the common factor.

$3 x + 4 (\frac{- 27}{4}) = 16$

$y = - \frac{27}{4}$

Step 2.2.1.3

Rewrite the expression.

$3 x - 27 = 16$

$y = - \frac{27}{4}$

$3 x - 27 = 16$

$y = - \frac{27}{4}$

$3 x - 27 = 16$

$y = - \frac{27}{4}$

$3 x - 27 = 16$

$y = - \frac{27}{4}$

Step 3

Solve for $x$ in $3 x - 27 = 16$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $27$ to both sides of the equation.

$3 x = 16 + 27$

$y = - \frac{27}{4}$

Step 3.1.2

Add $16$ and $27$ .

$3 x = 43$

$y = - \frac{27}{4}$

$3 x = 43$

$y = - \frac{27}{4}$

Step 3.2

Divide each term in $3 x = 43$ by $3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $3 x = 43$ by $3$ .

$\frac{3 x}{3} = \frac{43}{3}$

$y = - \frac{27}{4}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{43}{3}$

$y = - \frac{27}{4}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{43}{3}$

$y = - \frac{27}{4}$

$x = \frac{43}{3}$

$y = - \frac{27}{4}$

$x = \frac{43}{3}$

$y = - \frac{27}{4}$

$x = \frac{43}{3}$

$y = - \frac{27}{4}$

$x = \frac{43}{3}$

$y = - \frac{27}{4}$

Step 4

Solve the system of equations.

$x = \frac{43}{3} y = - \frac{27}{4}$

Step 5

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

$(\frac{43}{3}, - \frac{27}{4})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{43}{3}, - \frac{27}{4})$

Equation Form:

$x = \frac{43}{3}, y = - \frac{27}{4}$

Step 7