Precalculus Examples

$3 x - y = 7$ , $- 3 x + y = 5$

Step 1

Add $3 x$ to both sides of the equation.

$y = 5 + 3 x$

$3 x - y = 7$

Step 2

Replace all occurrences of $y$ with $5 + 3 x$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $3 x - y = 7$ with $5 + 3 x$ .

$3 x - (5 + 3 x) = 7$

$y = 5 + 3 x$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $3 x - (5 + 3 x)$ .

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.

$3 x - 1 \cdot 5 - (3 x) = 7$

$y = 5 + 3 x$

Step 2.2.1.1.2

Multiply $- 1$ by $5$ .

$3 x - 5 - (3 x) = 7$

$y = 5 + 3 x$

Step 2.2.1.1.3

Multiply $3$ by $- 1$ .

$3 x - 5 - 3 x = 7$

$y = 5 + 3 x$

$3 x - 5 - 3 x = 7$

$y = 5 + 3 x$

Step 2.2.1.2

Combine the opposite terms in $3 x - 5 - 3 x$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $3 x$ from $3 x$ .

$0 - 5 = 7$

$y = 5 + 3 x$

Step 2.2.1.2.2

Subtract $5$ from $0$ .

$- 5 = 7$

$y = 5 + 3 x$

$- 5 = 7$

$y = 5 + 3 x$

$- 5 = 7$

$y = 5 + 3 x$

$- 5 = 7$

$y = 5 + 3 x$

$- 5 = 7$

$y = 5 + 3 x$

Step 3

Since $- 5 = 7$ is not true, there is no solution.

No solution

Step 4