Solve the System of Equations 3x-y=17 and x+4y=23

$3 x - y = 17$ and $x + 4 y = 23$

Step 1

Subtract $4 y$ from both sides of the equation.

$x = 23 - 4 y$

$3 x - y = 17$

Step 2

Replace all occurrences of $x$ with $23 - 4 y$ in each equation.

Replace all occurrences of $x$ in $3 x - y = 17$ with $23 - 4 y$ .

$3 (23 - 4 y) - y = 17$

$x = 23 - 4 y$

Simplify the left side.

Simplify $3 (23 - 4 y) - y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 23 + 3 (- 4 y) - y = 17$

$x = 23 - 4 y$

Multiply $3$ by $23$ .

$69 + 3 (- 4 y) - y = 17$

$x = 23 - 4 y$

Multiply $- 4$ by $3$ .

$69 - 12 y - y = 17$

$x = 23 - 4 y$

$69 - 12 y - y = 17$

$x = 23 - 4 y$

Subtract $y$ from $- 12 y$ .

$69 - 13 y = 17$

$x = 23 - 4 y$

$69 - 13 y = 17$

$x = 23 - 4 y$

$69 - 13 y = 17$

$x = 23 - 4 y$

$69 - 13 y = 17$

$x = 23 - 4 y$

Step 3

Solve for $y$ in $69 - 13 y = 17$ .

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

Subtract $69$ from both sides of the equation.

$- 13 y = 17 - 69$

$x = 23 - 4 y$

Subtract $69$ from $17$ .

$- 13 y = - 52$

$x = 23 - 4 y$

$- 13 y = - 52$

$x = 23 - 4 y$

Divide each term in $- 13 y = - 52$ by $- 13$ and simplify.

Divide each term in $- 13 y = - 52$ by $- 13$ .

$\frac{- 13 y}{- 13} = \frac{- 52}{- 13}$

$x = 23 - 4 y$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 y}{- 13} = \frac{- 52}{- 13}$

$x = 23 - 4 y$

Divide $y$ by $1$ .

$y = \frac{- 52}{- 13}$

$x = 23 - 4 y$

$y = \frac{- 52}{- 13}$

$x = 23 - 4 y$

$y = \frac{- 52}{- 13}$

$x = 23 - 4 y$

Simplify the right side.

Divide $- 52$ by $- 13$ .

$y = 4$

$x = 23 - 4 y$

$y = 4$

$x = 23 - 4 y$

$y = 4$

$x = 23 - 4 y$

$y = 4$

$x = 23 - 4 y$

Step 4

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

Replace all occurrences of $y$ in $x = 23 - 4 y$ with $4$ .

$x = 23 - 4 \cdot 4$

$y = 4$

Simplify the right side.

Simplify $23 - 4 \cdot 4$ .

Multiply $- 4$ by $4$ .

$x = 23 - 16$

$y = 4$

Subtract $16$ from $23$ .

$x = 7$

$y = 4$

$x = 7$

$y = 4$

$x = 7$

$y = 4$

$x = 7$

$y = 4$

Step 5

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

$(7, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, 4)$

Equation Form:

$x = 7, y = 4$

Step 7

Solve the System of Equations 3x-y=17 and x+4y=23

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