Solve the following simultaneous equations: 2x + y = 5 ; x²+y² = 5
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0
Answer:
Substitute
y
=
3
x
+
1
in
x
2
+
y
2
=
5
to obtain
x
2
+
(
3
x
+
1
)
2
=
5
⇒
10
x
2
+
6
x
−
4
=
0
Hence
5
x
2
+
3
x
−
2
=
0
⇒
5
x
2
+
5
x
−
2
x
−
2
=
0
⇒
5
x
(
x
+
1
)
−
2
(
x
+
1
)
=
0
⇒
(
5
x
−
2
)
(
x
+
1
)
=
0
Hence
either
x
=
2
5
,
y
=
3
×
2
5
+
1
=
11
5
or
x
=
−
1
,
y
=
3
×
(
−
1
)
+
1
=
−
2
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