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

$y = 4 x - 2$ $y = x + 3$

Eliminate the equal sides of each equation and combine.

$4 x - 2 = x + 3$

Solve $4 x - 2 = x + 3$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$4 x - 2 - x = 3$

Subtract $x$ from $4 x$ .

$3 x - 2 = 3$

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

Add $2$ to both sides of the equation.

$3 x = 3 + 2$

Add $3$ and $2$ .

$3 x = 5$

Divide each term in $3 x = 5$ by $3$ and simplify.

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Evaluate $y$ when $x = \frac{5}{3}$ .

Substitute $\frac{5}{3}$ for $x$ .

$y = (\frac{5}{3}) + 3$

Substitute $\frac{5}{3}$ for $x$ in $y = (\frac{5}{3}) + 3$ and solve for $y$ .

Remove parentheses.

$y = \frac{5}{3} + 3$

Remove parentheses.

$y = (\frac{5}{3}) + 3$

Simplify $(\frac{5}{3}) + 3$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{5}{3} + 3 \cdot \frac{3}{3}$

Combine $3$ and $\frac{3}{3}$ .

$y = \frac{5}{3} + \frac{3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{5 + 3 \cdot 3}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$y = \frac{5 + 9}{3}$

Add $5$ and $9$ .

$y = \frac{14}{3}$

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

$(\frac{5}{3}, \frac{14}{3})$

The result can be shown in multiple forms.

Point Form:

$(\frac{5}{3}, \frac{14}{3})$

Equation Form:

$x = \frac{5}{3}, y = \frac{14}{3}$

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

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