Solve by Substitution y=3x+1 , 3y-4x=13

$y = 3 x + 1$ , $3 y - 4 x = 13$

Step 1

Replace all occurrences of $y$ with $3 x + 1$ in each equation.

Replace all occurrences of $y$ in $3 y - 4 x = 13$ with $3 x + 1$ .

$3 (3 x + 1) - 4 x = 13$

$y = 3 x + 1$

Simplify the left side.

Simplify $3 (3 x + 1) - 4 x$ .

Simplify each term.

Apply the distributive property.

$3 (3 x) + 3 \cdot 1 - 4 x = 13$

$y = 3 x + 1$

Multiply $3$ by $3$ .

$9 x + 3 \cdot 1 - 4 x = 13$

$y = 3 x + 1$

Multiply $3$ by $1$ .

$9 x + 3 - 4 x = 13$

$y = 3 x + 1$

$9 x + 3 - 4 x = 13$

$y = 3 x + 1$

Subtract $4 x$ from $9 x$ .

$5 x + 3 = 13$

$y = 3 x + 1$

$5 x + 3 = 13$

$y = 3 x + 1$

$5 x + 3 = 13$

$y = 3 x + 1$

$5 x + 3 = 13$

$y = 3 x + 1$

Step 2

Solve for $x$ in $5 x + 3 = 13$ .

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

Subtract $3$ from both sides of the equation.

$5 x = 13 - 3$

$y = 3 x + 1$

Subtract $3$ from $13$ .

$5 x = 10$

$y = 3 x + 1$

$5 x = 10$

$y = 3 x + 1$

Divide each term in $5 x = 10$ by $5$ and simplify.

Divide each term in $5 x = 10$ by $5$ .

$\frac{5 x}{5} = \frac{10}{5}$

$y = 3 x + 1$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{10}{5}$

$y = 3 x + 1$

Divide $x$ by $1$ .

$x = \frac{10}{5}$

$y = 3 x + 1$

$x = \frac{10}{5}$

$y = 3 x + 1$

$x = \frac{10}{5}$

$y = 3 x + 1$

Simplify the right side.

Divide $10$ by $5$ .

$x = 2$

$y = 3 x + 1$

$x = 2$

$y = 3 x + 1$

$x = 2$

$y = 3 x + 1$

$x = 2$

$y = 3 x + 1$

Step 3

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

Replace all occurrences of $x$ in $y = 3 x + 1$ with $2$ .

$y = 3 (2) + 1$

$x = 2$

Simplify the right side.

Simplify $3 (2) + 1$ .

Multiply $3$ by $2$ .

$y = 6 + 1$

$x = 2$

Add $6$ and $1$ .

$y = 7$

$x = 2$

$y = 7$

$x = 2$

$y = 7$

$x = 2$

$y = 7$

$x = 2$

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=3x+1 , 3y-4x=13

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