19. Solve: 3x + y = 15
2x - y = 5
Answers
Answer:
Using the method of simultaneous equations, you take the first equation and write
y
in terms of
x
to get
y
=
−
3
x
−
26
Then you substitute this into the second equation, ie. wherever you see a
y
in the second equation, you replace it with
(
−
3
x
−
26
)
. This yields
2
x
−
(
−
3
x
−
26
)
=
−
19
This then leaves an equation with only one unknown,
x
, so we may solve or
x
to obtain
5
x
+
26
=
−
19
Therefore
x
=
−
9
.
Then substitute back to get the value or
y
as
−
3
⋅
(
−
9
)
−
26
=
1
An alternative method would be to use linear matrix algebra, in which a separate 3 methods exist :
Gauss-Jordan elimination
Inverse matrix method
Kramer's Rule
Please let me know if you require me to resolve the problem using any of these 3 methods and I will do so for you, otherwise the simultaneous equation method shown above should suffice or a
2
×
2
linear system. The matrix methods are more time efficient for higher order systems like
3
×
3
and higher.
Answer:
x=4
y=3
Step-by-step explanation:
solving given equations
We get
5x=20
x=4
sub x value in one equation
we get 2(4)-y=5
8-y=5
-y=-3
y=3