Solve by Substitution y=5x+1 , 2y-6x=10

$y = 5 x + 1$ , $2 y - 6 x = 10$

Step 1

Replace all occurrences of $y$ with $5 x + 1$ in each equation.

Replace all occurrences of $y$ in $2 y - 6 x = 10$ with $5 x + 1$ .

$2 (5 x + 1) - 6 x = 10$

$y = 5 x + 1$

Simplify the left side.

Simplify $2 (5 x + 1) - 6 x$ .

Simplify each term.

Apply the distributive property.

$2 (5 x) + 2 \cdot 1 - 6 x = 10$

$y = 5 x + 1$

Multiply $5$ by $2$ .

$10 x + 2 \cdot 1 - 6 x = 10$

$y = 5 x + 1$

Multiply $2$ by $1$ .

$10 x + 2 - 6 x = 10$

$y = 5 x + 1$

$10 x + 2 - 6 x = 10$

$y = 5 x + 1$

Subtract $6 x$ from $10 x$ .

$4 x + 2 = 10$

$y = 5 x + 1$

$4 x + 2 = 10$

$y = 5 x + 1$

$4 x + 2 = 10$

$y = 5 x + 1$

$4 x + 2 = 10$

$y = 5 x + 1$

Step 2

Solve for $x$ in $4 x + 2 = 10$ .

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

Subtract $2$ from both sides of the equation.

$4 x = 10 - 2$

$y = 5 x + 1$

Subtract $2$ from $10$ .

$4 x = 8$

$y = 5 x + 1$

$4 x = 8$

$y = 5 x + 1$

Divide each term in $4 x = 8$ by $4$ and simplify.

Divide each term in $4 x = 8$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4}$

$y = 5 x + 1$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4}$

$y = 5 x + 1$

Divide $x$ by $1$ .

$x = \frac{8}{4}$

$y = 5 x + 1$

$x = \frac{8}{4}$

$y = 5 x + 1$

$x = \frac{8}{4}$

$y = 5 x + 1$

Simplify the right side.

Divide $8$ by $4$ .

$x = 2$

$y = 5 x + 1$

$x = 2$

$y = 5 x + 1$

$x = 2$

$y = 5 x + 1$

$x = 2$

$y = 5 x + 1$

Step 3

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

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

$y = 5 (2) + 1$

$x = 2$

Simplify the right side.

Simplify $5 (2) + 1$ .

Multiply $5$ by $2$ .

$y = 10 + 1$

$x = 2$

Add $10$ and $1$ .

$y = 11$

$x = 2$

$y = 11$

$x = 2$

$y = 11$

$x = 2$

$y = 11$

$x = 2$

Step 4

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

$(2, 11)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 11)$

Equation Form:

$x = 2, y = 11$

Step 6

Solve by Substitution y=5x+1 , 2y-6x=10

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