Solve the System of Equations x-y=0 5x-2y=6

$x - y = 0$ $5 x - 2 y = 6$

Step 1

Add $y$ to both sides of the equation.

$x = y$

$5 x - 2 y = 6$

Step 2

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

Replace all occurrences of $x$ in $5 x - 2 y = 6$ with $y$ .

$5 (y) - 2 y = 6$

$x = y$

Simplify the left side.

Subtract $2 y$ from $5 y$ .

$3 y = 6$

$x = y$

$3 y = 6$

$x = y$

$3 y = 6$

$x = y$

Step 3

Divide each term in $3 y = 6$ by $3$ and simplify.

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

$x = y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

$x = y$

Divide $y$ by $1$ .

$y = \frac{6}{3}$

$x = y$

$y = \frac{6}{3}$

$x = y$

$y = \frac{6}{3}$

$x = y$

Simplify the right side.

Divide $6$ by $3$ .

$y = 2$

$x = y$

$y = 2$

$x = y$

$y = 2$

$x = y$

Step 4

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

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

$x = 2$

$y = 2$

Simplify the left side.

Remove parentheses.

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

Step 5

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

$(2, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 2)$

Equation Form:

$x = 2, y = 2$

Step 7

Solve the System of Equations x-y=0 5x-2y=6

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