To solve the system of linear equations by graphing, follow these steps:
1. Write down the given equations:
[tex]\[
\begin{array}{l}
y = -0.25x + 4.7 \\
y = 4.9x - 1.64
\end{array}
\][/tex]
2. Graph the first equation: \(y = -0.25x + 4.7\)
- This equation represents a straight line with a slope of \(-0.25\) and a y-intercept of \(4.7\).
- Plot the y-intercept: \( (0, 4.7) \).
- Use the slope to find another point:
- The slope \(-0.25\) means that for each unit increase in \(x\), \(y\) decreases by \(0.25\).
- Moving from \( (0, 4.7) \) one unit to the right (increase \(x\) by 1), \(y\) decreases by 0.25, so the point is \( (1, 4.45) \).
3. Graph the second equation: \(y = 4.9x - 1.64\)
- This equation represents a straight line with a slope of \(4.9\) and a y-intercept of \(-1.64\).
- Plot the y-intercept: \( (0, -1.64) \).
- Use the slope to find another point:
- The slope \(4.9\) means that for each unit increase in \(x\), \(y\) increases by \(4.9\).
- Moving from \( (0, -1.64) \) one unit to the right (increase \(x\) by 1), \(y\) increases by 4.9, so the point is \( (1, 3.26) \).
4. Draw the lines on a coordinate plane:
- Plot the points \( (0, 4.7) \) and \( (1, 4.45) \) for the first line and connect them with a straight line.
- Plot the points \( (0, -1.64) \) and \( (1, 3.26) \) for the second line and connect them with a straight line.
5. Find the intersection point:
- The intersection of the lines represents the solution to the system of equations.
- By looking at the graph, identify the point where the two lines intersect.
6. Round the solution to the nearest tenth:
- Upon graphing, we find the intersection occurs approximately at the point \( (1.2, 4.4) \).
Therefore, the approximate solution to the system of equations is:
[tex]\[
\boxed{(1.2, 4.4)}
\][/tex]
