Solving systems of equations Problem set B Answers

\(x=-1,\ y=4\)

1. (a) \(4x^2 + 23x - 21=0\)
2. (b) \(3x^2 - 5x - 8=0\)

1. (a) \(x=\frac{17}{47},\ y=-\frac{118}{47}\) (x = 0.362, y = −2.51 to 3 s.f.)
2. (b) \(x=\frac{35}{11},\ y=\frac{17}{11}\) (x = 3.18, y = 1.55 to 3 s.f.)

\(x=-2,\ y=3,\ z=1\)

\(x=\frac{10}{11},\ y=-\frac{5}{11},\ z=-\frac{17}{11}\) (x = 0.909, y = −0.455, z = −1.55 to 3 s.f.)

\(w=-1,\ x=2,\ y=1,\ z=-2\)

\(w=-\frac{1}{6},\ x=-\frac{19}{39},\ y=\frac{97}{78},\ z=\frac{55}{26}\) (w = −0.167, x = −0.487, y = 1.24, z = 2.12 to 3 s.f.)

1. (a) No solution
2. (b) Infinitely many solutions
3. (c) \(k = 5\)

1. (a) \(3a + 2b=18.5,\ 5a + 3b=29.45\)
2. (b) $23.40

\(u_1=6,\ d=4\)

\(u_1=\frac{3}{2},\ d=\frac{5}{4}\)