Question

From the graph shown, what is an approximate solution of the system of equations?

Two intersecting lines graphed on a coordinate plane. The lines intersect at the point that is just past 1 on the x axis and just above 3 on the y aixs.

y = −0.5x + 4
y = 1 + 2x
A. (1.25, 3.4)
B. (2.25, 3.4)
C. (3.4, 1.25)
D. (3.4, 2.25)

Answer 1

To find the approximate solution of the system of equations represented by the two lines, we need to determine where they intersect.

The equations of the lines are:
1. \( y = -0.5x + 4 \)
2. \( y = 1 + 2x \)

We can solve for the intersection point by setting the two equations equal to each other:

\[
-0.5x + 4 = 1 + 2x
\]

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

1. First, add \(0.5x\) to both sides:
\[
4 = 1 + 2x + 0.5x
\]
\[
4 = 1 + 2.5x
\]

2. Next, subtract \(1\) from both sides:
\[
4 - 1 = 2.5x
\]
\[
3 = 2.5x
\]

3. Now, divide by \(2.5\):
\[
x = \frac{3}{2.5}
\]
\[
x = 1.2
\]

Now, substitute \(x = 1.2\) back into one of the original equations to find \(y\). We can use the first equation:

\[
y = -0.5(1.2) + 4
\]
\[
y = -0.6 + 4
\]
\[
y = 3.4
\]

Thus, the intersection point is approximately \((1.2, 3.4)\).

Looking at the options provided, the point that is just past 1 on the x-axis and just above 3 on the y-axis is closest to:

**A. (1.25, 3.4)**

So, the final answer is **A. (1.25, 3.4)**.