1
\begin{cases} h^2k - 100 = 0 \\ k^2h + 80 = 0 \end{cases} Give each set as (h, k).
Chapter 25 · Systems Solvable by Quadratics
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
0first-try
0of 10 done
From Dividing One Equation by the Other, exercise 4
Solve (using division where possible), pair results, and check.
From Dividing One Equation by the Other, exercise 1
Solve (using division where possible), pair results, and check.
2
\begin{cases} x^{2} - y^{2} = 16 \\ x + y = 8 \end{cases}
From Special Devices: Squares of Sums and Differences, exercise 3
Solve in a manner similar to that of the two preceding examples, pair results, and check each rational set of roots.
3
\begin{cases} x^{2} + 4 y^{2} = 41 \\ x y + 10 = 0 \end{cases}
From Problems Leading to Quadratic Systems, exercise 12
Reject all results which do not satisfy the conditions of the problems. Where two answers both satisfy a problem, give both.
4
The volumes of two cubes differ by 1647 cubic inches. Their edges differ by 3 inches. Find the edge of each.
From One Equation Linear, One Quadratic, exercise 5
Solve the following systems, pair results, and check each set of roots.
5
\begin{cases} x y + 12 = 0 \\ 4 x - 3 y = 30 \end{cases}
From Geometrical Problems, exercise 8
6
The bases of a trapezoid are 10 and 16 respectively, and the two nonparallel sides are 25 and 29. Find the altitude of the trapezoid and the area.
From Problems Leading to Quadratic Systems, exercise 17
Reject all results which do not satisfy the conditions of the problems. Where two answers both satisfy a problem, give both.
7
Do positive integers differing by 3 exist such that the sum of their squares is 115?
From Special Devices: Squares of Sums and Differences, exercise 10
Solve in a manner similar to that of the two preceding examples, pair results, and check each rational set of roots.
8
\begin{cases} x^{2} = y^{2} + 5 \\ y^{2} + x y = 10 \end{cases}
From Geometrical Problems, exercise 5
9
The sides of a triangle are 11, 13, and 20. Find the altitude on the side 11 and the area of the triangle.
From Dividing One Equation by the Other, exercise 6
Solve (using division where possible), pair results, and check.
10
\begin{cases} \dfrac{gt^2}{2} = .0256 \\[4pt] gt = 1.28 \end{cases} Give each set as (g, t).