3x=y-4 ; 2x+y=-1 solve by graphically method
Answers
Answer:
Explanation:
For each of the equations we can find two points on the line and then draw a line through the points to graph the line.
Equation 1
For
x
=
0
:
(
2
⋅
0
)
−
y
=
4
0
−
y
=
4
−
y
=
4
−
1
×
−
y
=
−
1
×
4
y
=
−
4
or
(
0
,
−
4
)
For
x
=
2
(
2
⋅
2
)
−
y
=
4
4
−
y
=
4
−
4
+
4
−
y
=
−
4
+
4
0
−
y
=
0
−
y
=
0
−
1
×
−
y
=
−
1
×
0
y
=
0
or
(
2
,
0
)
graph{(x^2+(y+4)^2-0.05)((x-2)^2+y^2-0.05)(2x-y-4)=0 [-15, 15, -7.5, 7.5]}
Equation 2
For
x
=
0
:
(
3
⋅
0
)
+
y
=
1
0
+
y
=
1
y
=
1
or
(
0
,
1
)
For
x
=
2
(
3
⋅
2
)
+
y
=
1
6
+
y
=
1
−
6
+
6
+
y
=
−
6
+
1
0
+
y
=
−
5
y
=
−
5
or
(
2
,
−
5
)
graph{(3x+y-1)(x^2+(y-1)^2-0.05)((x-2)^2+(y+5)^2-0.05)(2x-y-4)=0 [-15, 15, -7.5, 7.5]}
Solution
We can see the lines cross at
(
1
,
−
2
)
Therefore:
The system is consistent because it has at least one solution. And, it is independent because the lines have different slopes.
graph{(3x+y-1)((x-1)^2+(y+2)^2-0.015)(2x-y-4)=0 [-6, 6, -3, 3]}