Solve by Substitution -5x+3y=2 y=2x

$- 5 x + 3 y = 2$ $y = 2 x$

Step 1

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

Replace all occurrences of $y$ in $- 5 x + 3 y = 2$ with $2 x$ .

$- 5 x + 3 (2 x) = 2$

$y = 2 x$

Simplify the left side.

Simplify $- 5 x + 3 (2 x)$ .

Multiply $2$ by $3$ .

$- 5 x + 6 x = 2$

$y = 2 x$

Add $- 5 x$ and $6 x$ .

$x = 2$

$y = 2 x$

$x = 2$

$y = 2 x$

$x = 2$

$y = 2 x$

$x = 2$

$y = 2 x$

Step 2

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

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

$y = 2 (2)$

$x = 2$

Simplify the right side.

Multiply $2$ by $2$ .

$y = 4$

$x = 2$

$y = 4$

$x = 2$

$y = 4$

$x = 2$

Step 3

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

$(2, 4)$

Step 4

The result can be shown in multiple forms.

Point Form:

$(2, 4)$

Equation Form:

$x = 2, y = 4$

Step 5