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Mathematics
Mathematics
Problem
Consider the system of simultaneous equations
{
x
=
k
−
2
y
y
=
−
1
2
x
+
2
.
\begin{cases} x = k - 2y \\ y = -\frac{1}{2}x + 2 \end{cases}.
{
x
=
k
−
2
y
y
=
−
2
1
x
+
2
.
a. a** Find the gradient of each line. b. b** Find the value(s) of
k
k
k
such that the system has:
i
no solutions
ii
infinitely many solutions. Interpret these cases geometrically.
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