Solve the System of Equations y=2x+1 and y=4x-1

$y = 2 x + 1$ and $y = 4 x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x + 1 = 4 x - 1$

Step 2

Solve $2 x + 1 = 4 x - 1$ for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$2 x + 1 - 4 x = - 1$

Subtract $4 x$ from $2 x$ .

$- 2 x + 1 = - 1$

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

Subtract $1$ from both sides of the equation.

$- 2 x = - 1 - 1$

Subtract $1$ from $- 1$ .

$- 2 x = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = 4 (1) - 1$

Simplify $4 (1) - 1$ .

Multiply $4$ by $1$ .

$y = 4 - 1$

Subtract $1$ from $4$ .

$y = 3$

Step 4

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

$(1, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 6

Solve the System of Equations y=2x+1 and y=4x-1

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