Solve by Substitution x+2y=200 , x=y+50

$x + 2 y = 200$ , $x = y + 50$

Step 1

Replace all occurrences of $x$ with $y + 50$ in each equation.

Replace all occurrences of $x$ in $x + 2 y = 200$ with $y + 50$ .

$(y + 50) + 2 y = 200$

$x = y + 50$

Simplify the left side.

Add $y$ and $2 y$ .

$3 y + 50 = 200$

$x = y + 50$

$3 y + 50 = 200$

$x = y + 50$

$3 y + 50 = 200$

$x = y + 50$

Step 2

Solve for $y$ in $3 y + 50 = 200$ .

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

Subtract $50$ from both sides of the equation.

$3 y = 200 - 50$

$x = y + 50$

Subtract $50$ from $200$ .

$3 y = 150$

$x = y + 50$

$3 y = 150$

$x = y + 50$

Divide each term in $3 y = 150$ by $3$ and simplify.

Divide each term in $3 y = 150$ by $3$ .

$\frac{3 y}{3} = \frac{150}{3}$

$x = y + 50$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{150}{3}$

$x = y + 50$

Divide $y$ by $1$ .

$y = \frac{150}{3}$

$x = y + 50$

$y = \frac{150}{3}$

$x = y + 50$

$y = \frac{150}{3}$

$x = y + 50$

Simplify the right side.

Divide $150$ by $3$ .

$y = 50$

$x = y + 50$

$y = 50$

$x = y + 50$

$y = 50$

$x = y + 50$

$y = 50$

$x = y + 50$

Step 3

Replace all occurrences of $y$ with $50$ in each equation.

Replace all occurrences of $y$ in $x = y + 50$ with $50$ .

$x = (50) + 50$

$y = 50$

Simplify the right side.

Add $50$ and $50$ .

$x = 100$

$y = 50$

$x = 100$

$y = 50$

$x = 100$

$y = 50$

Step 4

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

$(100, 50)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(100, 50)$

Equation Form:

$x = 100, y = 50$

Step 6

Solve by Substitution x+2y=200 , x=y+50

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