Solve the System of Equations -10x+3y=5 x=y-4

$- 10 x + 3 y = 5$ $x = y - 4$

Step 1

Replace all occurrences of $x$ with $y - 4$ in each equation.

Replace all occurrences of $x$ in $- 10 x + 3 y = 5$ with $y - 4$ .

$- 10 (y - 4) + 3 y = 5$

$x = y - 4$

Simplify the left side.

Simplify $- 10 (y - 4) + 3 y$ .

Simplify each term.

Apply the distributive property.

$- 10 y - 10 \cdot - 4 + 3 y = 5$

$x = y - 4$

Multiply $- 10$ by $- 4$ .

$- 10 y + 40 + 3 y = 5$

$x = y - 4$

$- 10 y + 40 + 3 y = 5$

$x = y - 4$

Add $- 10 y$ and $3 y$ .

$- 7 y + 40 = 5$

$x = y - 4$

$- 7 y + 40 = 5$

$x = y - 4$

$- 7 y + 40 = 5$

$x = y - 4$

$- 7 y + 40 = 5$

$x = y - 4$

Step 2

Solve for $y$ in $- 7 y + 40 = 5$ .

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

Subtract $40$ from both sides of the equation.

$- 7 y = 5 - 40$

$x = y - 4$

Subtract $40$ from $5$ .

$- 7 y = - 35$

$x = y - 4$

$- 7 y = - 35$

$x = y - 4$

Divide each term in $- 7 y = - 35$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 35$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 35}{- 7}$

$x = y - 4$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 35}{- 7}$

$x = y - 4$

Divide $y$ by $1$ .

$y = \frac{- 35}{- 7}$

$x = y - 4$

$y = \frac{- 35}{- 7}$

$x = y - 4$

$y = \frac{- 35}{- 7}$

$x = y - 4$

Simplify the right side.

Divide $- 35$ by $- 7$ .

$y = 5$

$x = y - 4$

$y = 5$

$x = y - 4$

$y = 5$

$x = y - 4$

$y = 5$

$x = y - 4$

Step 3

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

Replace all occurrences of $y$ in $x = y - 4$ with $5$ .

$x = (5) - 4$

$y = 5$

Simplify the right side.

Subtract $4$ from $5$ .

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

Step 4

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

$(1, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 5)$

Equation Form:

$x = 1, y = 5$

Step 6

Solve the System of Equations -10x+3y=5 x=y-4

Related Questions

Support LCMGCF.com by disabling your adblocker.