To solve the system of equations using graphing, follow these steps:
Given the system of equations:
1. \(\frac{7}{3} x + y = 0.4\)
2. \(0.6 x - y = 4\)
Step-by-Step Solution:
1. Rewrite the equations in slope-intercept form (\(y = mx + b\)).
For the first equation:
[tex]\[\frac{7}{3} x + y = 0.4\][/tex]
Isolate \( y \):
[tex]\[y = -\frac{7}{3} x + 0.4\][/tex]
For the second equation:
\(0.6 x - y = 4\)
Isolate \( y \):
[tex]\[y = 0.6 x - 4\][/tex]
2. Graph the two equations:
- The first equation: \( y = -\frac{7}{3} x + 0.4 \)
- This is a line with a slope of \(-\frac{7}{3}\) and y-intercept at \(0.4\).
- The second equation: \( y = 0.6 x - 4 \)
- This is a line with a slope of \(0.6\) and y-intercept at \(-4\).
3. Find the point of intersection of these two lines.
Using a graphing calculator, plot both equations:
[tex]\[ y = -\frac{7}{3} x + 0.4 \][/tex]
[tex]\[ y = 0.6 x - 4 \][/tex]
4. Determine the coordinates of the intersection point:
The graphing calculator reveals the intersection of the two lines which represents the solution to the system of equations.
The intersection point (solution) is approximately:
[tex]\[ \left(1.500, -3.100\right) \][/tex]
Thus, the solution set is [tex]\( \{ (1.500, -3.100) \} \)[/tex].
