Question

📝Practice Screen #29.
Drag and drop the points to graph and solve the system of equations.




y =
2
3​x−2 (blue line)

=-\frac{1}{2}x+
y=−
1
2​x+5 (red line)



✅ CORRECT!

Enter the solution:

Answer 1

To solve the system of equations graphically, let’s first identify the two equations we will be working with:

1. **Blue Line:** \( y = \frac{2}{3}x - 2 \)
2. **Red Line:** \( y = -\frac{1}{2}x + 5 \)

To find the solution of the system, we need to determine the point where these two lines intersect.

### Step 1: Find the Intersection Point

To find the point of intersection, set the two equations equal to each other:

\[
\frac{2}{3}x - 2 = -\frac{1}{2}x + 5
\]

### Step 2: Solve for \( x \)

Multiply every term by 6 to eliminate the fractions:

\[
6 \left(\frac{2}{3}x\right) - 6(2) = 6\left(-\frac{1}{2}x\right) + 6(5)
\]

This simplifies to:

\[
4x - 12 = -3x + 30
\]

Now, combine like terms:

\[
4x + 3x = 30 + 12
\]

\[
7x = 42
\]

Now, divide by 7:

\[
x = 6
\]

### Step 3: Substitute \( x \) Back to Find \( y \)

Now, we can substitute \( x = 6 \) back into either equation to find \( y \). Let’s use the blue line equation:

\[
y = \frac{2}{3}(6) - 2
\]

Calculating this gives:

\[
y = 4 - 2 = 2
\]

### Solution

Thus, the solution to the system of equations, or the point of intersection, is:

**(6, 2)**

You can then enter the solution as:

**Enter the solution:** \( (6, 2) \)