A system of linear equations contains two equations with negative reciprocal
1 answer:
let's recall that perpendicular lines have negative reciprocal slopes, so say for a line with a slope of a/b
a perpendicular one will be -b/a.
what does that mean? well, that the lines are perpendicular of course, they meet at a 90° angle, and two straight lines meeting at 90° can only meet once.
since a solution to a system of equations is where the graph meet, and these two meet perpendicularly once, then that means only one solution.
You might be interested in
Answer:
Graphs Attached Below
Step-by-step explanation:
Hello!
Standard form of a quadratic:
From our Equation:
- a = 1/2
- b = -2
- c = 0
There are several values that are needed to drawing a parabola:
- y - intercept
- Axis of Symmetry (AOS)
- Vertex
- x - intercepts
Standard form of a quadratic:
The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.
<h2>Axis of Symmetry</h2>A parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.
To calculate the AOS, we use the formula , from the values of the equation.
Calculate
The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.
<h2>Vertex</h2>The vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.
To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.
Calculate
The y-value is -2. The vertex is (2, -2).
<h2>X-intercepts</h2>The x-intercepts are the points where the graph intersects the x-axis (y = 0).
Solve by Factoring
The roots are (0,0) and (4,0).
<h2>Graph</h2>Now we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.
<em>Image Attached</em>
<h2>Domain Restrictions</h2>The Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.
That means we remove the parts of the line that don't belong in that domain.
<em>Image Attached</em>
