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The intersection points of lines that represent the equations in a system of linear equations shows the solutions of the system.
Start by writing the equations in slope-intercept form.
Recall the definition of a negative reciprocal.
Number of Solutions: One solution
Explanation: See solution.
Slopes: 34 and - 43
y-intercepts: 1 and - 2
Relationship Between the Slopes: They are negative reciprocals
The Value of m: - 2
Explanation: The slopes of two perpendicular lines are negative reciprocals
We want to find the number of solutions to this system of equations. Note that the lines described by the equations of the system intersect at a point.
The point of intersection solves the system of linear equations. This means that the system has one solution.
y=3/4x+1 y=-4/3x-2 ⇒ y= 3/4x+ 1 y= -4/3x+( - 2) We can now identify the desired parts.
| Equations | Slope | y-intercept |
|---|---|---|
| y= 3/4x+ 1 | 3/4 | 1 |
| y= -4/3x+( - 2) | -4/3 | - 2 |
Notice that the slopes of two perpendicular lines are negative reciprocals of each other.
1/2 negative reciprocal → -2/1 The value of m is -2.