Question

Question

Watch Video

Show Examples
Find the solution of the system of equations.
minus, 6, x, plus, 6, y, equals, minus, 24
−6x+6y=
−24
minus, 6, x, plus, 9, y, equals, minus, 45
−6x+9y=
−45

Answer 1

To solve the system of equations:

1. \(-6x + 6y = -24\) (Equation 1)
2. \(-6x + 9y = -45\) (Equation 2)

We can use the elimination method.

### Step 1: Simplify the equations
First, we can simplify both equations by dividing them by the coefficients of \(x\).

For Equation 1:
\[
-6x + 6y = -24 \quad \text{(dividing by -6)}
\]
\[
x - y = 4 \quad \text{(Equation 3)}
\]

For Equation 2:
\[
-6x + 9y = -45 \quad \text{(dividing by -6)}
\]
\[
x - \frac{3}{2}y = \frac{15}{2} \quad \text{(Equation 4)}
\]

### Step 2: Solve for one variable
Now we can use Equation 3 to express \(x\) in terms of \(y\):
\[
x = y + 4
\]

### Step 3: Substitute into the other equation
Substituting \(x\) from Equation 3 into Equation 4:
\[
(y + 4) - \frac{3}{2}y = \frac{15}{2}
\]

To clear the fractions, multiply the whole equation by 2:
\[
2(y + 4) - 3y = 15
\]
\[
2y + 8 - 3y = 15
\]
\[
-y + 8 = 15
\]
Rearranging gives:
\[
-y = 15 - 8
\]
\[
-y = 7
\]
Multiplying through by -1:
\[
y = -7
\]

### Step 4: Find \(x\)
Now substitute \(y\) back into Equation 3 to find \(x\):
\[
x = -7 + 4 = -3
\]

### Solution
The solution to the system of equations is:
\[
x = -3, \quad y = -7
\]

Thus, the solution is \((x, y) = (-3, -7)\).