By Agnes Musyoki
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Extra info for An Elementary Swahili Newspaper Reader
The following examples illustrate the solution of equations and inequalitiesinvolving absolutevalues. EXAMPLE l-: Solve for x: lar+ 2l:5. solurroN: This equation will be satisfiedif either 3x*2:5 or -(3r*2):5 Considering each equation separatellr w€ have x: L and x: -& which are the two solutions to the given equation. uxluplr 2: Solve for x: lz*- rl: l4x+ 31. solurroN: This equation will be satisfiedif either 2x-L-4x*3 or 2x-1--Gx+j\ Solving the first equation, w€ have x: -2; solving the second,we get x: -*, thus giving us two solutions to the original equation.
Thus, P is the point (4, 3). 18 So, an equation of the circle is (x-l)'+ (Y-6)': (\ft)' or, equivalently, F i g u r e1 . 6 . 6 /- )Exercises In Exercises 1 through 4, find an equation of the circle with center at C and radius r. Write the equation in both the centerradius forrr and the gmeral form. ' , . c ( Q ,0 ) , r : 8 r . c 1 4 , - 3 ) ,r : S 3. C(-5, -12), f :3 4. C(-l,l),r:2 In Exercises5 through 10, find an equation of the circle satisfying the given condition$. 5. Center is at (1, 2\ and through the point (3, -1).
5 Definition are symmetric with respect to R. 5 it follows that if a point (x, y) is on a graph which is symmetric with respect to the x axis, then the point (x,-y) also must be on the graph. And, if both the points (x,y) and (x,-y) are on the graph, then the graph is symmetric with respect to the x axis. Therefore, the coordinates of the point (x,-y) as well as (x, y) must satisfy an equation of the graph. Hence, we may conclude that the graph of an equation in r and y is symmetric with respect to the r axis if and only if an equivalent equation is obtained when y is replaced by -y in the equation.
An Elementary Swahili Newspaper Reader by Agnes Musyoki