Finite Math Examples

$- x + y = - 1$ , $3 x - 2 y = 0$ , $2 x - y = 4$

Step 1

Add $x$ to both sides of the equation.

$y = - 1 + x$

$3 x - 2 y = 0$

$2 x - y = 4$

Step 2

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

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $3 x - 2 y = 0$ with $- 1 + x$ .

$3 x - 2 (- 1 + x) = 0$

$y = - 1 + x$

$2 x - y = 4$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $3 x - 2 (- 1 + x)$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$3 x - 2 \cdot - 1 - 2 x = 0$

$y = - 1 + x$

$2 x - y = 4$

Step 2.2.1.1.2

Multiply $- 2$ by $- 1$ .

$3 x + 2 - 2 x = 0$

$y = - 1 + x$

$2 x - y = 4$

$3 x + 2 - 2 x = 0$

$y = - 1 + x$

$2 x - y = 4$

Step 2.2.1.2

Subtract $2 x$ from $3 x$ .

$x + 2 = 0$

$y = - 1 + x$

$2 x - y = 4$

$x + 2 = 0$

$y = - 1 + x$

$2 x - y = 4$

$x + 2 = 0$

$y = - 1 + x$

$2 x - y = 4$

Step 2.3

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

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

$x + 2 = 0$

$y = - 1 + x$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $2 x - (- 1 + x)$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Apply the distributive property.

$2 x + 1 - x = 4$

$x + 2 = 0$

$y = - 1 + x$

Step 2.4.1.1.2

Multiply $- 1$ by $- 1$ .

$2 x + 1 - x = 4$

$x + 2 = 0$

$y = - 1 + x$

$2 x + 1 - x = 4$

$x + 2 = 0$

$y = - 1 + x$

Step 2.4.1.2

Subtract $x$ from $2 x$ .

$x + 1 = 4$

$x + 2 = 0$

$y = - 1 + x$

$x + 1 = 4$

$x + 2 = 0$

$y = - 1 + x$

$x + 1 = 4$

$x + 2 = 0$

$y = - 1 + x$

$x + 1 = 4$

$x + 2 = 0$

$y = - 1 + x$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $1$ from both sides of the equation.

$x = 4 - 1$

$x + 2 = 0$

$y = - 1 + x$

Step 3.2

Subtract $1$ from $4$ .

$x = 3$

$x + 2 = 0$

$y = - 1 + x$

$x = 3$

$x + 2 = 0$

$y = - 1 + x$

Step 4

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

Tap for more steps...

Step 4.1

Replace all occurrences of $x$ in $x + 2 = 0$ with $3$ .

$(3) + 2 = 0$

$x = 3$

$y = - 1 + x$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Add $3$ and $2$ .

$5 = 0$

$x = 3$

$y = - 1 + x$

$5 = 0$

$x = 3$

$y = - 1 + x$

Step 4.3

Replace all occurrences of $x$ in $y = - 1 + x$ with $3$ .

$y = - 1 + 3$

$5 = 0$

$x = 3$

Step 4.4

Simplify $y = - 1 + 3$ .

Tap for more steps...

Step 4.4.1

Simplify the left side.

Tap for more steps...

Step 4.4.1.1

Remove parentheses.

$y = - 1 + 3$

$5 = 0$

$x = 3$

$y = - 1 + 3$

$5 = 0$

$x = 3$

Step 4.4.2

Simplify the right side.

Tap for more steps...

Step 4.4.2.1

Add $- 1$ and $3$ .

$y = 2$

$5 = 0$

$x = 3$

$y = 2$

$5 = 0$

$x = 3$

$y = 2$

$5 = 0$

$x = 3$

$y = 2$

$5 = 0$

$x = 3$

Step 5

Since $5 = 0$ is not true, there is no solution.

No solution

Step 6