The system of linear equations y equals three halves times x minus 3 and y equals negative one half times x plus 4 is graphed on a coordinate plane. Approximate the solution to the system.

Question

coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 4 comma 3 and 0 comma negative 3
(−1.5, −3.5)
(−1.5, 4.25)
(2.5, 1.5)
(3.5, 2.25)

Answer 1

To approximate the solution to the system of linear equations given by the lines:

1. \( y = \frac{3}{2}x - 3\)
2. \( y = -\frac{1}{2}x + 4\)

we can identify the intersection point by finding the values of \(x\) and \(y\) that satisfy both equations simultaneously.

To do this, we can set the equations equal to each other:

\[ \frac{3}{2}x - 3 = -\frac{1}{2}x + 4 \]

Next, combine the \(x\) terms:

\[ \frac{3}{2}x + \frac{1}{2}x = 4 + 3 \]

This simplifies to:

\[ 2x = 7 \]

So,

\[ x = \frac{7}{2} = 3.5 \]

Now, substitute \(x = 3.5\) back into one of the original equations to find \(y\). We'll use the first equation:

\[ y = \frac{3}{2}(3.5) - 3 \]

Calculating this gives:

\[ y = \frac{3 \times 3.5}{2} - 3 = \frac{10.5}{2} - 3 = 5.25 - 3 = 2.25 \]

Thus, the approximate solution to the system of equations occurs at the point \( (3.5, 2.25) \).

So, the correct answer from the provided options is:

(3.5, 2.25).