To solve the system of linear equations by graphing, we can start with the two equations:
- \( y = -0.25x + 4.7 \)
- \( y = 4.9x - 1.64 \)
Next, let's graph both equations:
1. Graphing the first equation: \( y = -0.25x + 4.7 \)
- The y-intercept is \( 4.7 \) (where the line crosses the y-axis).
- The slope is \( -0.25 \), which means for every increase of 1 in \( x \), \( y \) decreases by \( 0.25 \).
Points for the first line:
- When \( x = 0 \): \( y = 4.7 \) (point: \( (0, 4.7) \))
- When \( x = 4 \): \( y = -0.25(4) + 4.7 = 4.7 - 1 = 3.7 \) (point: \( (4, 3.7) \))
2. Graphing the second equation: \( y = 4.9x - 1.64 \)
- The y-intercept is \( -1.64 \).
- The slope is \( 4.9 \), which means for every increase of 1 in \( x \), \( y \) increases by \( 4.9 \).
Points for the second line:
- When \( x = 0 \): \( y = -1.64 \) (point: \( (0, -1.64) \))
- When \( x = 1 \): \( y = 4.9(1) - 1.64 = 4.9 - 1.64 = 3.26 \) (point: \( (1, 3.26) \))
Graphing the lines:
- Plot the points for each equation.
- Draw the lines for both equations.
Finding the approximate intersection:
To find the intersection point accurately, we can set the equations equal to each other:
\[ -0.25x + 4.7 = 4.9x - 1.64 \]
Rearranging gives: \[ 4.7 + 1.64 = 4.9x + 0.25x \] \[ 6.34 = 5.15x \]
Now, solve for \( x \): \[ x \approx \frac{6.34}{5.15} \approx 1.23 \]
Substituting \( x \) back into one of the original equations to find \( y \): Using the first equation: \[ y = -0.25(1.23) + 4.7 \approx -0.3075 + 4.7 \approx 4.3925 \]
Rounding:
Rounding the approximated values to the nearest tenth gives us:
- \( x \approx 1.2 \)
- \( y \approx 4.4 \)
Thus, the approximate solution to the system is: \[ (1.2, 4.4) \]
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