graphicaly ,the oair of equations 8x-16y+28=0, 2z -4y + 7 =o rwpresent the two lines which are
Answers
Answer:
A zero of a function f is a number a such that f(a) = 0. In other words, a zero of f is a solution for the equation f(x) = 0. Furthermore, x = a is a zero of f if and only if the point (a,0) is an x-intercept of the graph of f.
Given any equation in x, there is an equivalent equation of the form f(x) = 0. Solving the equation is the same as finding the zeros of f, which is the same as finding the x-intercepts of the graph of the equation.
Example 1.
Problem: Solve 5x + 2 = 3x - 7
Subtracting 3x and adding 7 to both sides of the equation yields the equivalent equation:
2x + 9 = 0.
So, the following three problems are equivalent:
Solve 5x + 2 = 3x - 7.
Find the zeros of f(x) = 2x + 9.
Find the x-intercepts of y = 2x + 9.
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Solving Equations Graphically
The fact that solving equations may be thought of as finding the x-intercepts of a graph makes graphing utilities very useful for equation solving. You should understand that in most cases, a graphing utility will not find the exact solutions of an equation, merely approximations.
Example 2.
Approximate the solutions for x3 + 5x = 2x2 + 7.
The first step is to rewrite the equation in "f(x) = 0 form"; iI.e., move all the terms to one side of the equation. Using the notation required by the Java Grapher, we have
x^3 + 5*x - 2*x^2 - 7 = 0.
Now graph the function f(x) = x^3 + 5*x - 2*x^2 - 7.
Step-by-step explanation:
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a2= 2 b2 = -4 c2 = 7
=> a1/a2 = 8/2= 4 , b1/b2 = -16/-4 = 4 , c1/c2 = 28/7 = 4
=> a1/a2 = b1/b2 = c1/c2
So , the two lines are coincident line