Question

What is the solution of: (7/2) x - (9/2) = 2y and 4y = 7x - 9
A. (1.286, 0) and (0, -2.25)
B. (1.286, 0)

Answer 1

To solve the system of equations given:

1. \(\frac{7}{2} x - \frac{9}{2} = 2y\)
2. \(4y = 7x - 9\)

We can rearrange the first equation to express \(y\) in terms of \(x\):

\[
\frac{7}{2} x - \frac{9}{2} = 2y
\]

Dividing everything by 2, we have:

\[
\frac{7}{4} x - \frac{9}{4} = y
\]

Now, we can substitute this expression for \(y\) into the second equation:

\[
4y = 7x - 9
\]

Substituting \(y\):

\[
4\left(\frac{7}{4} x - \frac{9}{4}\right) = 7x - 9
\]

This simplifies to:

\[
7x - 9 = 7x - 9
\]

This equation is true for all \(x\), which means that there are infinitely many solutions along the line defined by these two equations.

To find the intersection points, we can solve for specific values. Let's find the y-intercept by setting \(x = 0\):

From \(y = \frac{7}{4} x - \frac{9}{4}\):

\[
y = \frac{7}{4}(0) - \frac{9}{4} = -\frac{9}{4} = -2.25
\]

So one solution is \((0, -2.25)\).

Now, let’s find another specific solution. Set \(y = 0\):

\[
0 = \frac{7}{4} x - \frac{9}{4}
\]

Solving for \(x\):

\[
\frac{7}{4} x = \frac{9}{4}
\]
\[
x = \frac{9}{7} \approx 1.2857 \approx 1.286
\]

So another solution is \((1.286, 0)\).

Thus, the two solution points we found are:

1. \((1.286, 0)\)
2. \((0, -2.25)\)

The correct answer is:

**A. (1.286, 0) and (0, -2.25)**.