Find k if the equation are consistent 2x + 3 y - 2 = 0 ,2 X + 4 y - k = 0, X- 2y + 3 k =0
Answers
Answer:
Step-by-step explanation:
k= -2
Answer:
k
=
−
2
Explanation:
Since equations are consistent, we find values of
x
and
y
first and then substitute them in the equation to find value of
k
.
x
+
3
y
+
2
=
0
-------> equation 1
4
y
+
2
x
=
k
----------> equation 2
x
−
2
y
=
3
------------> equation 3
From equation 1; make
x
the subject.
x
−
2
y
=
3
x
=
3
+
2
y
Substitute
x
=
3
+
2
y
in equation 1
x
+
3
y
+
2
=
0
(
3
+
2
y
)
+
3
y
+
2
=
0
3
+
2
y
+
3
y
+
2
=
0
3
+
5
y
+
2
=
0
5
y
=
−
2
−
3
5
y
=
−
5
y
=
−
1
Now, substitute value of
y
=
−
1
in equation 3 to get value of
x
x
−
2
y
=
3
x
−
2
(
−
1
)
=
3
x
+
2
=
3
x
=
3
−
2
x
=
1
Check the answer of values of
x
and
y
before finding value of
k
x
+
3
y
+
2
=
0
1
+
3
(
−
1
)
+
2
=
0
1
−
3
+
2
=
0
−
2
+
2
=
0
------> so values of
x
and
y
are correct.
Final step is to substitute values of
x
and
y
in equation 2 to find value of
k
:
4
y
+
2
x
=
k
4
(
−
1
)
+
2
(
1
)
=
k
−
4
+
2
=
k
−
2
=
k
Therefore,
k
=
−
2