
Question 4
Use the ALEKS graphing calculator to solve the system of equations.y=11xc-6
y=-2x-2
Round to the nearest hundredth.

Let's solve the system of equations using algebraic methods:

We are given two equations:
1. \( y = 11x - 6 \)
2. \( y = -2x - 2 \)

### Step 1: Set the equations equal to each other
Since both equations are equal to \( y \), we can set them equal to each other:
\[
11x - 6 = -2x - 2
\]

### Step 2: Solve for \( x \)
Move all terms involving \( x \) to one side and constants to the other:
\[
11x + 2x = -2 + 6
\]
\[
13x = 4
\]

Now, solve for \( x \):
\[
x = \frac{4}{13} \approx 0.31
\]

### Step 3: Solve for \( y \)
Substitute \( x = 0.31 \) into one of the original equations to solve for \( y \). Let's use the first equation:
\[
y = 11(0.31) - 6
\]
\[
y = 3.41 - 6
\]
\[
y = -2.59
\]

### Final Answer:
The solution to the system of equations is approximately \( (x, y) = (0.31, -2.59) \).

Would you like more details or have any other questions?

Here are 5 related questions you might explore:
1. How do you graph two equations to find their intersection point?
2. What are other methods for solving systems of linear equations?
3. How do you interpret the solution of a system graphically?
4. What happens if the system of equations has no solution or infinitely many solutions?
5. How can you check your solution by substituting the values back into the original equations?

**Tip:** When solving systems of equations, double-check your steps by substituting the solution back into both original equations to verify!

Use the ALEKS graphing calculator to solve the system of equations. y = 11x - 6 and y = -2x - 2. Round to the nearest hundredth.

Discover how to solve the system of equations y = 11x - 6 and y = -2x - 2 using algebraic methods. Learn step-by-step how to find the intersection point by equating the two equations and solving for x and y. This problem involves key concepts in solving systems of linear equations and is suitable for students in Grades 8-10.

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