Ask a New Question
Menu

–x + y = 4

–2x − 3y = 18

(, )

1 answer

To solve the system of equations given by:

  1. \(-x + y = 4\)

  2. \(-2x - 3y = 18\)

we can solve for \(y\) in terms of \(x\) using the first equation, and then substitute that into the second equation.

Step 1: Solve for \(y\) in the first equation

From equation (1):

\[ y = x + 4 \]

Step 2: Substitute \(y\) into the second equation

Now substitute \(y\) in equation (2):

\[ -2x - 3(x + 4) = 18 \]

Step 3: Simplify and solve for \(x\)

Distributing on the left side:

\[ -2x - 3x - 12 = 18 \] \[ -5x - 12 = 18 \]

Now, add 12 to both sides:

\[ -5x = 30 \]

Now divide by -5:

\[ x = -6 \]

Step 4: Find \(y\) using the value of \(x\)

Now substitute \(x = -6\) back into the equation for \(y\):

\[ y = -6 + 4 = -2 \]

Solution

The solution to the system of equations is:

\[ (x, y) = (-6, -2) \]

So the final answer is \((-6, -2)\).