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

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

Step 1

Solve for $x$ in $2 x - y = 1$ .

Add $y$ to both sides of the equation.

$2 x = 1 + y$

$4 x - 2 y = 2$

Divide each term in $2 x = 1 + y$ by $2$ and simplify.

Divide each term in $2 x = 1 + y$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

Divide $x$ by $1$ .

$x = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$4 x - 2 y = 2$

Step 2

Replace all occurrences of $x$ with $\frac{1}{2} + \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $4 x - 2 y = 2$ with $\frac{1}{2} + \frac{y}{2}$ .

$4 (\frac{1}{2} + \frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Simplify the left side.

Simplify $4 (\frac{1}{2} + \frac{y}{2}) - 2 y$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{1}{2}) + 4 (\frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) (\frac{1}{2}) + 4 (\frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Cancel the common factor.

$2 \cdot (2 (\frac{1}{2})) + 4 (\frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Rewrite the expression.

$2 + 4 (\frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 + 4 (\frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 + 2 (2) (\frac{y}{2}) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Cancel the common factor.

$2 + 2 \cdot (2 (\frac{y}{2})) - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Rewrite the expression.

$2 + 2 y - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 + 2 y - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 + 2 y - 2 y = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Combine the opposite terms in $2 + 2 y - 2 y$ .

Subtract $2 y$ from $2 y$ .

$2 + 0 = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Add $2$ and $0$ .

$2 = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 = 2$

$x = \frac{1}{2} + \frac{y}{2}$

$2 = 2$

$x = \frac{1}{2} + \frac{y}{2}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{1}{2} + \frac{y}{2}$

Step 4

Related Questions