Solve the System of Equations 3x+y=-5 6x+2y=10

$3 x + y = - 5$ $6 x + 2 y = 10$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = - 5 - 3 x$

$6 x + 2 y = 10$

Step 2

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

Replace all occurrences of $y$ in $6 x + 2 y = 10$ with $- 5 - 3 x$ .

$6 x + 2 (- 5 - 3 x) = 10$

$y = - 5 - 3 x$

Simplify the left side.

Simplify $6 x + 2 (- 5 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$6 x + 2 \cdot - 5 + 2 (- 3 x) = 10$

$y = - 5 - 3 x$

Multiply $2$ by $- 5$ .

$6 x - 10 + 2 (- 3 x) = 10$

$y = - 5 - 3 x$

Multiply $- 3$ by $2$ .

$6 x - 10 - 6 x = 10$

$y = - 5 - 3 x$

$6 x - 10 - 6 x = 10$

$y = - 5 - 3 x$

Combine the opposite terms in $6 x - 10 - 6 x$ .

Subtract $6 x$ from $6 x$ .

$0 - 10 = 10$

$y = - 5 - 3 x$

Subtract $10$ from $0$ .

$- 10 = 10$

$y = - 5 - 3 x$

$- 10 = 10$

$y = - 5 - 3 x$

$- 10 = 10$

$y = - 5 - 3 x$

$- 10 = 10$

$y = - 5 - 3 x$

$- 10 = 10$

$y = - 5 - 3 x$

Step 3

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

No solution

Step 4