Solve by Substitution y=2x+1 , 5y-7x=11

$y = 2 x + 1$ , $5 y - 7 x = 11$

Step 1

Replace all occurrences of $y$ with $2 x + 1$ in each equation.

Replace all occurrences of $y$ in $5 y - 7 x = 11$ with $2 x + 1$ .

$5 (2 x + 1) - 7 x = 11$

$y = 2 x + 1$

Simplify the left side.

Simplify $5 (2 x + 1) - 7 x$ .

Simplify each term.

Apply the distributive property.

$5 (2 x) + 5 \cdot 1 - 7 x = 11$

$y = 2 x + 1$

Multiply $2$ by $5$ .

$10 x + 5 \cdot 1 - 7 x = 11$

$y = 2 x + 1$

Multiply $5$ by $1$ .

$10 x + 5 - 7 x = 11$

$y = 2 x + 1$

$10 x + 5 - 7 x = 11$

$y = 2 x + 1$

Subtract $7 x$ from $10 x$ .

$3 x + 5 = 11$

$y = 2 x + 1$

$3 x + 5 = 11$

$y = 2 x + 1$

$3 x + 5 = 11$

$y = 2 x + 1$

$3 x + 5 = 11$

$y = 2 x + 1$

Step 2

Solve for $x$ in $3 x + 5 = 11$ .

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

Subtract $5$ from both sides of the equation.

$3 x = 11 - 5$

$y = 2 x + 1$

Subtract $5$ from $11$ .

$3 x = 6$

$y = 2 x + 1$

$3 x = 6$

$y = 2 x + 1$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

$y = 2 x + 1$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

$y = 2 x + 1$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

$y = 2 x + 1$

$x = \frac{6}{3}$

$y = 2 x + 1$

$x = \frac{6}{3}$

$y = 2 x + 1$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

$y = 2 x + 1$

$x = 2$

$y = 2 x + 1$

$x = 2$

$y = 2 x + 1$

$x = 2$

$y = 2 x + 1$

Step 3

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

Replace all occurrences of $x$ in $y = 2 x + 1$ with $2$ .

$y = 2 (2) + 1$

$x = 2$

Simplify the right side.

Simplify $2 (2) + 1$ .

Multiply $2$ by $2$ .

$y = 4 + 1$

$x = 2$

Add $4$ and $1$ .

$y = 5$

$x = 2$

$y = 5$

$x = 2$

$y = 5$

$x = 2$

$y = 5$

$x = 2$

Step 4

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

$(2, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Step 6

Solve by Substitution y=2x+1 , 5y-7x=11

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