Система \left \{ {{a_1x+b_1y=c_1} \atop {a_2x+b_2y=c_2}} \right.{
a
2
x+b
2
y=c
2
a
1
x+b
1
y=c
1
не имеет решений, если выполняется соотношение:
\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}
a
2
a
1
=
b
2
b
1
=
c
2
c
1
\begin{gathered} \left \{ {{ax+12y=36} \atop {3x+ay=18}} \right. \; \; \Rightarrow \; \; \; \frac{a}{3}=\frac{12}{a}\ne \frac{36}{18}frac{a}{3}=\frac{12}{a}\ne \frac{2}{1}frac{a}{3}=\frac{12}{a}\; \; \to \; \; a^2=36\; ,\; \; a=\pm 6frac{12}{a}\ne 2\; \; \to \; \; \; a\ne 6frac{a}{3}\ne 2\; \; \to \; \; a\ne 6text{\O}tvet:\; \; a=-6\; . \end{gathered}
{
3x+ay=18
ax+12y=36
⇒
3
a
=
a
12
=
18
36
3
a
=
a
12
=
1
2
3
a
=
a
12
→a
2
=36,a=±6
a
12
=2→a
=6
3
a
=2→a
=6
text\Otvet:a=−6.
