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

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

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

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

$2 x + 3 x - 1 = 4$

$y = 3 x - 1$

Simplify the left side.

Simplify $2 x + 3 x - 1$ .

Remove parentheses.

$2 x + 3 x - 1 = 4$

$y = 3 x - 1$

Add $2 x$ and $3 x$ .

$5 x - 1 = 4$

$y = 3 x - 1$

$5 x - 1 = 4$

$y = 3 x - 1$

$5 x - 1 = 4$

$y = 3 x - 1$

$5 x - 1 = 4$

$y = 3 x - 1$

Solve for $x$ in $5 x - 1 = 4$ .

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

Add $1$ to both sides of the equation.

$5 x = 4 + 1$

$y = 3 x - 1$

Add $4$ and $1$ .

$5 x = 5$

$y = 3 x - 1$

$5 x = 5$

$y = 3 x - 1$

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

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

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

$y = 3 x - 1$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$y = 3 x - 1$

Divide $x$ by $1$ .

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

$y = 3 x - 1$

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

$y = 3 x - 1$

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

$y = 3 x - 1$

Simplify the right side.

Divide $5$ by $5$ .

$x = 1$

$y = 3 x - 1$

$x = 1$

$y = 3 x - 1$

$x = 1$

$y = 3 x - 1$

$x = 1$

$y = 3 x - 1$

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

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

$y = 3 (1) - 1$

$x = 1$

Simplify the right side.

Simplify $3 (1) - 1$ .

Multiply $3$ by $1$ .

$y = 3 - 1$

$x = 1$

Subtract $1$ from $3$ .

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

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

$(1, 2)$

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

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

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