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 is not an ordered pair

Answer 1

To solve the system of equations given by:

1. \( y = \frac{2}{3}x - 2 \) (blue line)
2. \( y = -\frac{1}{2}x + 5 \) (red line)

we can find the solution by setting the two equations equal to each other because they both equal \( y \).

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

Now, let's solve for \( x \).

1. First, let's eliminate the fractions by multiplying every term by 6, the least common multiple of the denominators (3 and 2):

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

This simplifies to:

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

2. Next, add \( 3x \) to both sides:

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

This simplifies to:

\[
7x - 12 = 30
\]

3. Now, add 12 to both sides:

\[
7x = 42
\]

4. Divide by 7:

\[
x = 6
\]

Now that we have \( x \), we can find \( y \) by plugging \( x \) back into either of the original equations. We can use the first equation:

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

Calculating this gives:

\[
y = 4 - 2 = 2
\]

The solution to the system of equations is the ordered pair \( (6, 2) \).

If you're required to express the answer in a different format (as you mentioned "Answer is not an ordered pair"), please clarify or specify the format needed.