College algebra . tion is of the form Av? -{-Cy^ + F^Q. If, instead of x and y, we consider x^ and y^ as the unknowns,the niethod of solution is that for linear equations. Aht. 53] SOLUTION OF SIMULTANEOUS QUADRATICS 77 EXERCISES Solve 1. 16 a2 +271/2 = 576, a;2 + j/2 = 25. Solution : Solving for ofi and y^ we have 676 27 16 676 3? — 25 1 -^.- y^ = 1 26 16 27 16 27 1 1 1 1 X = ±3. y = ±4. ^6. Hence, v?e find the following four solutions, (3,4), (-3,4), (3,-4), (-3, -4).To show these solutions graphically, we plot the loci of the two equations. - 1576-1625? 27 y = ± v25 — x!. The first equation
College algebra . tion is of the form Av? -{-Cy^ + F^Q. If, instead of x and y, we consider x^ and y^ as the unknowns,the niethod of solution is that for linear equations. Aht. 53] SOLUTION OF SIMULTANEOUS QUADRATICS 77 EXERCISES Solve 1. 16 a2 +271/2 = 576, a;2 + j/2 = 25. Solution : Solving for ofi and y^ we have 676 27 16 676 3? — 25 1 -^.- y^ = 1 26 16 27 16 27 1 1 1 1 X = ±3. y = ±4. ^6. Hence, v?e find the following four solutions, (3,4), (-3,4), (3,-4), (-3, -4).To show these solutions graphically, we plot the loci of the two equations. - 1576-1625? 27 y = ± v25 — x!. The first equation has for its locusthe oval-shaped figure A, B, C, D,called an ellipse, the second, thecircle (Fig. 12). The points of in-tersection represent graphically thefour pairs of solutions. If the lociof two equations do not intersect,the solutions of the equations willbe found to be imaginary. Plot and solve: 2. 9x2 + 25 3/2 = 225,*x2 + J/2 = 16. 3. 9x2 = 225,a;2 + 2/2 = 9. 5. 9x2 + 25^2 = 226,x2 + S = Fig. 12. :225, 4. 9x2 + 252/2 = x2 + 2/2 =; 9x2 + 252/2 = 225, 7. 4x2-92/2 = 36, 25x2 + 9 2/2 = 225. x2 + 2/2 = 16. Obtain to two significant figures the solutions of the following:8. + = 89, 9. + = , x2 + s/2 = x2 —2/2 = * The graph of 9 x2 + 25 2/2 = 225 is an ellipse of breadth 10 and height position with respect to the axes is similar to that of the ellipse in The graph of x2 + y2 = 16 is a circle of radius 4, and center at the in-tersection of the axes. 78 SIMULTANEOUS QUADRATICS [Chap. VII. Case II. When one of the equations is linear. EXERCISES Plot and solve1. a;2 + 2/2 . 8a; —4y —5 = 0,3x + 4y= : rrom the linear equation, 3Substituting in the quadratic equation and reducing, we have 5 2/^2 + 41/-28=0. Solving, we obtain —S Substituting these values in th! linear equation, we find a;4=^l,orV-The solutions are then (- 1, 2), (V-, - W-
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