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

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

Step 1

Divide each term in $2 x = - 10 y + 6$ by $2$ and simplify.

Divide each term in $2 x = - 10 y + 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 10 y}{2} + \frac{6}{2}$

$x + 5 y = 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 10 y}{2} + \frac{6}{2}$

$x + 5 y = 3$

Divide $x$ by $1$ .

$x = \frac{- 10 y}{2} + \frac{6}{2}$

$x + 5 y = 3$

$x = \frac{- 10 y}{2} + \frac{6}{2}$

$x + 5 y = 3$

$x = \frac{- 10 y}{2} + \frac{6}{2}$

$x + 5 y = 3$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 10$ and $2$ .

Factor $2$ out of $- 10 y$ .

$x = \frac{2 (- 5 y)}{2} + \frac{6}{2}$

$x + 5 y = 3$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (- 5 y)}{2 (1)} + \frac{6}{2}$

$x + 5 y = 3$

Cancel the common factor.

$x = \frac{2 (- 5 y)}{2 \cdot 1} + \frac{6}{2}$

$x + 5 y = 3$

Rewrite the expression.

$x = \frac{- 5 y}{1} + \frac{6}{2}$

$x + 5 y = 3$

Divide $- 5 y$ by $1$ .

$x = - 5 y + \frac{6}{2}$

$x + 5 y = 3$

$x = - 5 y + \frac{6}{2}$

$x + 5 y = 3$

$x = - 5 y + \frac{6}{2}$

$x + 5 y = 3$

Divide $6$ by $2$ .

$x = - 5 y + 3$

$x + 5 y = 3$

$x = - 5 y + 3$

$x + 5 y = 3$

$x = - 5 y + 3$

$x + 5 y = 3$

$x = - 5 y + 3$

$x + 5 y = 3$

Step 2

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

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

$(- 5 y + 3) + 5 y = 3$

$x = - 5 y + 3$

Simplify the left side.

Combine the opposite terms in $(- 5 y + 3) + 5 y$ .

Add $- 5 y$ and $5 y$ .

$0 + 3 = 3$

$x = - 5 y + 3$

Add $0$ and $3$ .

$3 = 3$

$x = - 5 y + 3$

$3 = 3$

$x = - 5 y + 3$

$3 = 3$

$x = - 5 y + 3$

$3 = 3$

$x = - 5 y + 3$

Step 3

Remove any equations from the system that are always true.

$x = - 5 y + 3$

Step 4

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

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