Solve by Substitution 2x+y=20 , 6x-5y=12

$2 x + y = 20$ , $6 x - 5 y = 12$

Step 1

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

$y = 20 - 2 x$

$6 x - 5 y = 12$

Step 2

Replace all occurrences of $y$ with $20 - 2 x$ in each equation.

Replace all occurrences of $y$ in $6 x - 5 y = 12$ with $20 - 2 x$ .

$6 x - 5 (20 - 2 x) = 12$

$y = 20 - 2 x$

Simplify the left side.

Simplify $6 x - 5 (20 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$6 x - 5 \cdot 20 - 5 (- 2 x) = 12$

$y = 20 - 2 x$

Multiply $- 5$ by $20$ .

$6 x - 100 - 5 (- 2 x) = 12$

$y = 20 - 2 x$

Multiply $- 2$ by $- 5$ .

$6 x - 100 + 10 x = 12$

$y = 20 - 2 x$

$6 x - 100 + 10 x = 12$

$y = 20 - 2 x$

Add $6 x$ and $10 x$ .

$16 x - 100 = 12$

$y = 20 - 2 x$

$16 x - 100 = 12$

$y = 20 - 2 x$

$16 x - 100 = 12$

$y = 20 - 2 x$

$16 x - 100 = 12$

$y = 20 - 2 x$

Step 3

Solve for $x$ in $16 x - 100 = 12$ .

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

Add $100$ to both sides of the equation.

$16 x = 12 + 100$

$y = 20 - 2 x$

Add $12$ and $100$ .

$16 x = 112$

$y = 20 - 2 x$

$16 x = 112$

$y = 20 - 2 x$

Divide each term in $16 x = 112$ by $16$ and simplify.

Divide each term in $16 x = 112$ by $16$ .

$\frac{16 x}{16} = \frac{112}{16}$

$y = 20 - 2 x$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{112}{16}$

$y = 20 - 2 x$

Divide $x$ by $1$ .

$x = \frac{112}{16}$

$y = 20 - 2 x$

$x = \frac{112}{16}$

$y = 20 - 2 x$

$x = \frac{112}{16}$

$y = 20 - 2 x$

Simplify the right side.

Divide $112$ by $16$ .

$x = 7$

$y = 20 - 2 x$

$x = 7$

$y = 20 - 2 x$

$x = 7$

$y = 20 - 2 x$

$x = 7$

$y = 20 - 2 x$

Step 4

Replace all occurrences of $x$ with $7$ in each equation.

Replace all occurrences of $x$ in $y = 20 - 2 x$ with $7$ .

$y = 20 - 2 \cdot 7$

$x = 7$

Simplify the right side.

Simplify $20 - 2 \cdot 7$ .

Multiply $- 2$ by $7$ .

$y = 20 - 14$

$x = 7$

Subtract $14$ from $20$ .

$y = 6$

$x = 7$

$y = 6$

$x = 7$

$y = 6$

$x = 7$

$y = 6$

$x = 7$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(7, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, 6)$

Equation Form:

$x = 7, y = 6$

Step 7

Solve by Substitution 2x+y=20 , 6x-5y=12

Related Questions

Support LCMGCF.com by disabling your adblocker.