Solve the System of Equations y=4x+1 3x+2y=13

$y = 4 x + 1$ $3 x + 2 y = 13$

Step 1

Replace all occurrences of $y$ with $4 x + 1$ in each equation.

Replace all occurrences of $y$ in $3 x + 2 y = 13$ with $4 x + 1$ .

$3 x + 2 (4 x + 1) = 13$

$y = 4 x + 1$

Simplify the left side.

Simplify $3 x + 2 (4 x + 1)$ .

Simplify each term.

Apply the distributive property.

$3 x + 2 (4 x) + 2 \cdot 1 = 13$

$y = 4 x + 1$

Multiply $4$ by $2$ .

$3 x + 8 x + 2 \cdot 1 = 13$

$y = 4 x + 1$

Multiply $2$ by $1$ .

$3 x + 8 x + 2 = 13$

$y = 4 x + 1$

$3 x + 8 x + 2 = 13$

$y = 4 x + 1$

Add $3 x$ and $8 x$ .

$11 x + 2 = 13$

$y = 4 x + 1$

$11 x + 2 = 13$

$y = 4 x + 1$

$11 x + 2 = 13$

$y = 4 x + 1$

$11 x + 2 = 13$

$y = 4 x + 1$

Step 2

Solve for $x$ in $11 x + 2 = 13$ .

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

Subtract $2$ from both sides of the equation.

$11 x = 13 - 2$

$y = 4 x + 1$

Subtract $2$ from $13$ .

$11 x = 11$

$y = 4 x + 1$

$11 x = 11$

$y = 4 x + 1$

Divide each term in $11 x = 11$ by $11$ and simplify.

Divide each term in $11 x = 11$ by $11$ .

$\frac{11 x}{11} = \frac{11}{11}$

$y = 4 x + 1$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{11}{11}$

$y = 4 x + 1$

Divide $x$ by $1$ .

$x = \frac{11}{11}$

$y = 4 x + 1$

$x = \frac{11}{11}$

$y = 4 x + 1$

$x = \frac{11}{11}$

$y = 4 x + 1$

Simplify the right side.

Divide $11$ by $11$ .

$x = 1$

$y = 4 x + 1$

$x = 1$

$y = 4 x + 1$

$x = 1$

$y = 4 x + 1$

$x = 1$

$y = 4 x + 1$

Step 3

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

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

$y = 4 (1) + 1$

$x = 1$

Simplify the right side.

Simplify $4 (1) + 1$ .

Multiply $4$ by $1$ .

$y = 4 + 1$

$x = 1$

Add $4$ and $1$ .

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

Step 4

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

$(1, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 5)$

Equation Form:

$x = 1, y = 5$

Step 6

Solve the System of Equations y=4x+1 3x+2y=13

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