Solve the System of Equations 2x+y=5 and x-3y=-8

$2 x + y = 5$ and $x - 3 y = - 8$

Subtract $2 x$ from both sides of the equation.

$y = 5 - 2 x$

$x - 3 y = - 8$

Replace all occurrences of $y$ with $5 - 2 x$ in each equation.

Replace all occurrences of $y$ in $x - 3 y = - 8$ with $5 - 2 x$ .

$x - 3 (5 - 2 x) = - 8$

$y = 5 - 2 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$x - 3 \cdot 5 - 3 (- 2 x) = - 8$

$y = 5 - 2 x$

Multiply $- 3$ by $5$ .

$x - 15 - 3 (- 2 x) = - 8$

$y = 5 - 2 x$

Multiply $- 2$ by $- 3$ .

$x - 15 + 6 x = - 8$

$y = 5 - 2 x$

$x - 15 + 6 x = - 8$

$y = 5 - 2 x$

Add $x$ and $6 x$ .

$7 x - 15 = - 8$

$y = 5 - 2 x$

$7 x - 15 = - 8$

$y = 5 - 2 x$

$7 x - 15 = - 8$

$y = 5 - 2 x$

$7 x - 15 = - 8$

$y = 5 - 2 x$

Solve for $x$ in $7 x - 15 = - 8$ .

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

Add $15$ to both sides of the equation.

$7 x = - 8 + 15$

$y = 5 - 2 x$

Add $- 8$ and $15$ .

$7 x = 7$

$y = 5 - 2 x$

$7 x = 7$

$y = 5 - 2 x$

Divide each term in $7 x = 7$ by $7$ and simplify.

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

$y = 5 - 2 x$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

$y = 5 - 2 x$

Divide $x$ by $1$ .

$x = \frac{7}{7}$

$y = 5 - 2 x$

$x = \frac{7}{7}$

$y = 5 - 2 x$

$x = \frac{7}{7}$

$y = 5 - 2 x$

Simplify the right side.

Divide $7$ by $7$ .

$x = 1$

$y = 5 - 2 x$

$x = 1$

$y = 5 - 2 x$

$x = 1$

$y = 5 - 2 x$

$x = 1$

$y = 5 - 2 x$

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

Replace all occurrences of $x$ in $y = 5 - 2 x$ with $1$ .

$y = 5 - 2 \cdot 1$

$x = 1$

Simplify the right side.

Simplify $5 - 2 \cdot 1$ .

Multiply $- 2$ by $1$ .

$y = 5 - 2$

$x = 1$

Subtract $2$ from $5$ .

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

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

$(1, 3)$

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Solve the System of Equations 2x+y=5 and x-3y=-8

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