Solving systems of equations Problem set A Answers

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

1. (a) \(6x^2 - 11x - 18=0\)
2. (b) \(2x^2 - 7x + 9=0\)

1. (a) \(x=2,\ y=-3\)
2. (b) \(x=\frac{23}{11},\ y=-\frac{31}{11}\) (x = 2.09, y = −2.82 to 3 s.f.)

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

\(x=\frac{5}{7},\ y=-\frac{2}{7},\ z=\frac{9}{7}\) (x = 0.714, y = −0.286, z = 1.29 to 3 s.f.)

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

\(w=\frac{25}{27},\ x=\frac{5}{2},\ y=\frac{7}{54},\ z=-\frac{1}{54}\) (w = 0.926, x = 2.50, y = 0.130, z = −0.0185 to 3 s.f.)

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

1. (a) \(2a + 5b=61.25,\ 3a + 4b=66.5\)
2. (b) $46.75

\(u_1=7,\ d=3\)

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