Question

Graph and then find the solution
y=5/8x-3 and -3/4x+8

Answer 1

To find the solution to the system of equations given by \( y = \frac{5}{8}x - 3 \) and \( y = -\frac{3}{4}x + 8 \), we start by plotting both equations on a graph and then find their intersection point, which gives us the solution to the system.

### Step 1: Graph the equations

1. **Equation 1:** \( y = \frac{5}{8}x - 3 \)
- The slope is \( \frac{5}{8} \) and the y-intercept is -3.
- To plot it, start from the y-intercept (0, -3).
- Then use the slope to find another point. For every 8 units you move to the right (increase in x), move up 5 units (increase in y).
- Points:
- (0, -3)
- (8, \frac{5}{8} \cdot 8 - 3) = (8, 5 - 3) = (8, 2)

2. **Equation 2:** \( y = -\frac{3}{4}x + 8 \)
- The slope is -\(\frac{3}{4}\) and the y-intercept is 8.
- Start at (0, 8).
- For this slope, for every 4 units you move to the right, move down 3 units.
- Points:
- (0, 8)
- (4, -\frac{3}{4} \cdot 4 + 8) = (4, -3 + 8) = (4, 5)

### Step 2: Intersection point

To find the intersection of the two lines, set the equations equal to each other:

\[
\frac{5}{8}x - 3 = -\frac{3}{4}x + 8
\]

### Step 3: Solve for \(x\)

1. Multiply through by 8 to eliminate the fractions:

\[
5x - 24 = -6x + 64
\]

2. Combine like terms:

\[
5x + 6x = 64 + 24
\]
\[
11x = 88
\]

3. Divide by 11:

\[
x = 8
\]

### Step 4: Find \(y\)

Now substitute \(x = 8\) into either of the original equations to find \(y\). Using the first equation:

\[
y = \frac{5}{8}(8) - 3 = 5 - 3 = 2
\]

### Conclusion

The solution to the system of equations is:

\[
\boxed{(8, 2)}
\]

This means that the two lines intersect at the point \((8, 2)\).