Precalculus Examples

$2 x + y = 6$ , $8 x + 4 y = 10$

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 6 - 2 x$

$8 x + 4 y = 10$

Step 2

Replace all occurrences of $y$ with $6 - 2 x$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $8 x + 4 y = 10$ with $6 - 2 x$ .

$8 x + 4 (6 - 2 x) = 10$

$y = 6 - 2 x$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $8 x + 4 (6 - 2 x)$ .

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.

$8 x + 4 \cdot 6 + 4 (- 2 x) = 10$

$y = 6 - 2 x$

Step 2.2.1.1.2

Multiply $4$ by $6$ .

$8 x + 24 + 4 (- 2 x) = 10$

$y = 6 - 2 x$

Step 2.2.1.1.3

Multiply $- 2$ by $4$ .

$8 x + 24 - 8 x = 10$

$y = 6 - 2 x$

$8 x + 24 - 8 x = 10$

$y = 6 - 2 x$

Step 2.2.1.2

Combine the opposite terms in $8 x + 24 - 8 x$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $8 x$ from $8 x$ .

$0 + 24 = 10$

$y = 6 - 2 x$

Step 2.2.1.2.2

Add $0$ and $24$ .

$24 = 10$

$y = 6 - 2 x$

$24 = 10$

$y = 6 - 2 x$

$24 = 10$

$y = 6 - 2 x$

$24 = 10$

$y = 6 - 2 x$

$24 = 10$

$y = 6 - 2 x$

Step 3

Since $24 = 10$ is not true, there is no solution.

No solution

Step 4