Question

A system of equations is shown.

y = 2.5x - 5
y = -0.75x + 3


Which of the following is the best estimate of the solution to the system of equations?

A. (2.5,1.1)
B. (1.3,2.4)
C. (0,3)
D. (4.6,6.4)

Answer 1

To find the best estimate of the solution to the system of equations, we can analyze where the two lines represented by the equations intersect.

The equations are:
1. \( y = 2.5x - 5 \)
2. \( y = -0.75x + 3 \)

To estimate the intersection point, we can set the two equations equal to each other:

\[
2.5x - 5 = -0.75x + 3
\]

Now, solve for \(x\):

\[
2.5x + 0.75x = 3 + 5
\]
\[
3.25x = 8
\]
\[
x = \frac{8}{3.25} \approx 2.46
\]

Now, substitute \(x \approx 2.46\) back into one of the original equations to find \(y\). We'll use the first equation:

\[
y = 2.5(2.46) - 5
\]
\[
y \approx 6.15 - 5 \approx 1.15
\]

Thus, the intersection point is approximately \((2.46, 1.15)\).

Now let's compare this estimate with the provided options:

A. (2.5, 1.1)
B. (1.3, 2.4)
C. (0, 3)
D. (4.6, 6.4)

The closest estimate to \((2.46, 1.15)\) is option **A: (2.5, 1.1)**.

So, the best estimate of the solution to the system of equations is **A. (2.5, 1.1)**.