To solve the system of linear equations graphically on your calculator, follow these steps:
1. Write the equations in slope-intercept form (y = mx + b):
The given system is:
```
4.78x + 5.16y = -29.30 ........ (1)
-2.84x + 2.26y = 10.23 ....... (2)
```
Let's convert each equation to the form y = mx + b.
2. Manipulate Equation (1):
```
4.78x + 5.16y = -29.30
5.16y = -4.78x - 29.30
y = (-4.78/5.16)x - 29.30/5.16
y = -0.92636x - 5.67829
```
3. Manipulate Equation (2):
```
-2.84x + 2.26y = 10.23
2.26y = 2.84x + 10.23
y = (2.84/2.26)x + 10.23/2.26
y = 1.25664x + 4.52743
```
4. Graph the equations:
Now you'll graph the two equations on your calculator (or graphing tool).
The first equation to graph would be:
```
y = -0.92636x - 5.67829
```
The second equation to graph would be:
```
y = 1.25664x + 4.52743
```
5. Identify the point of intersection:
When you input both equations into your graphing calculator and plot the graphs, find the point where the two lines intersect. This point of intersection represents the solution to the system of equations.
6. Select the correct solution:
Comparing the options given:
- (4.58, -2.42)
- (-4.66, -1.34)
- (-2.88, -0.90)
- (-2.21, -1.55)
The correct solution, determined graphically and which matches the calculated intersecting point from the derived equations, is:
```
(-4.66, -1.34)
```
Therefore, the correct choice is [tex]\((-4.66, -1.34)\)[/tex].
