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

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

Step 1

Subtract $5 x$ from both sides of the equation.

$y = 5 - 5 x$

$3 x + 2 y = 3$

Step 2

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

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

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

$y = 5 - 5 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = 5 - 5 x$

Multiply $2$ by $5$ .

$3 x + 10 + 2 (- 5 x) = 3$

$y = 5 - 5 x$

Multiply $- 5$ by $2$ .

$3 x + 10 - 10 x = 3$

$y = 5 - 5 x$

$3 x + 10 - 10 x = 3$

$y = 5 - 5 x$

Subtract $10 x$ from $3 x$ .

$- 7 x + 10 = 3$

$y = 5 - 5 x$

$- 7 x + 10 = 3$

$y = 5 - 5 x$

$- 7 x + 10 = 3$

$y = 5 - 5 x$

$- 7 x + 10 = 3$

$y = 5 - 5 x$

Step 3

Solve for $x$ in $- 7 x + 10 = 3$ .

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

Subtract $10$ from both sides of the equation.

$- 7 x = 3 - 10$

$y = 5 - 5 x$

Subtract $10$ from $3$ .

$- 7 x = - 7$

$y = 5 - 5 x$

$- 7 x = - 7$

$y = 5 - 5 x$

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

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

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

$y = 5 - 5 x$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

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

$y = 5 - 5 x$

Divide $x$ by $1$ .

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

$y = 5 - 5 x$

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

$y = 5 - 5 x$

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

$y = 5 - 5 x$

Simplify the right side.

Divide $- 7$ by $- 7$ .

$x = 1$

$y = 5 - 5 x$

$x = 1$

$y = 5 - 5 x$

$x = 1$

$y = 5 - 5 x$

$x = 1$

$y = 5 - 5 x$

Step 4

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

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

$y = 5 - 5 \cdot 1$

$x = 1$

Simplify the right side.

Simplify $5 - 5 \cdot 1$ .

Multiply $- 5$ by $1$ .

$y = 5 - 5$

$x = 1$

Subtract $5$ from $5$ .

$y = 0$

$x = 1$

$y = 0$

$x = 1$

$y = 0$

$x = 1$

$y = 0$

$x = 1$

Step 5

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

$(1, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 0)$

Equation Form:

$x = 1, y = 0$

Step 7

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

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