Solve by Substitution y=2x+3 , y=3x+1

$y = 2 x + 3$ , $y = 3 x + 1$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x + 3 = 3 x + 1$

Step 2

Solve $2 x + 3 = 3 x + 1$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

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

$2 x + 3 - 3 x = 1$

Subtract $3 x$ from $2 x$ .

$- x + 3 = 1$

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

Subtract $3$ from both sides of the equation.

$- x = 1 - 3$

Subtract $3$ from $1$ .

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

$y = 3 (2) + 1$

Simplify $3 (2) + 1$ .

Multiply $3$ by $2$ .

$y = 6 + 1$

Add $6$ and $1$ .

$y = 7$

Step 4

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

$(2, 7)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 7)$

Equation Form:

$x = 2, y = 7$

Step 6

Solve by Substitution y=2x+3 , y=3x+1

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