Prove graphically that system of equation 6x+4y=2 and 3x-2y=1 is consistent and dependent
Answers
Explanation:
Rewrite the system of linear equations given in slope-Intercept Form:
3
x
+
2
y
=
8
Equation.1
6
x
+
4
y
=
16
Equation.2
Equation.1 in Slope-Intercept Form:
3
x
+
2
y
=
8
Subtract
(
−
3
x
)
from both sides:
2
y
=
−
3
x
+
8
Divide both sides by
2
to obtain
y
=
(
1
2
)
⋅
(
−
3
x
+
8
)
Equation.3
Equation.2 in Slope-Intercept Form:
6
x
+
4
y
=
16
Subtract
(
−
6
x
)
from both sides
4
y
=
−
6
x
+
16
Divide both sides by
4
to obtain
y
=
(
1
4
)
⋅
(
−
6
x
+
16
)
Equation.4
Generate tables of values for both Equation.3 and Equation.4:
Explanation:
Rewrite the system of linear equations given in slope-Intercept Form:
3
x
+
2
y
=
8
Equation.1
6
x
+
4
y
=
16
Equation.2
Equation.1 in Slope-Intercept Form:
3
x
+
2
y
=
8
Subtract
(
−
3
x
)
from both sides:
2
y
=
−
3
x
+
8
Divide both sides by
2
to obtain
y
=
(
1
2
)
⋅
(
−
3
x
+
8
)
Equation.3
Equation.2 in Slope-Intercept Form:
6
x
+
4
y
=
16
Subtract
(
−
6
x
)
from both sides
4
y
=
−
6
x
+
16
Divide both sides by
4
to obtain
y
=
(
1
4
)
⋅
(
−
6
x
+
16
)
Equation.4
Generate tables of values for both Equation.3 and Equation.4:
The system of linear equations has at least one solution, and hence it is Consistent.
The given system of linear equations has an infinite number of solutions, hence it is also Dependent.
Hope it helps.
Answer:
\large\underline{\sf{Solution-}}
Solution−
Given pair of linear equations are
\red{\rm :\longmapsto\:6x + 4y = 2}:⟼6x+4y=2
and
\red{\rm :\longmapsto\:3x + 2y = 1}:⟼3x+2y=1
Consider Equation (1)
\red{\rm :\longmapsto\:6x + 4y = 2}:⟼6x+4y=2
Hᴇɴᴄᴇ,
➢ Pair of points of the given equation are shown in the below table.
\begin{gathered} \red{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0.5 \\ \\ \sf - 2 & \sf 3.5 \\ \\ \sf - 4 & \sf 6.5 \end{array}} \\ \end{gathered}}\end{gathered}
x
0
−2
−4
y
0.5
3.5
6.5
➢ Now draw a graph using the points
➢ See the attachment graph.
Consider Equation (2)
\green{\rm :\longmapsto\:3x + 2y = 1}:⟼3x+2y=1
Hᴇɴᴄᴇ,
➢ Pair of points of the given equation are shown in the below table.
\begin{gathered} \green{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0.5 \\ \\ \sf - 2 & \sf 3.5 \\ \\ \sf - 4 & \sf 6.5 \end{array}} \\ \end{gathered}}\end{gathered}
x
0
−2
−4
y
0.5
3.5
6.5
➢ Now draw a graph using the points
➢ See the attachment graph.
Hence, From graph we verified that given pair of lines are dependent and system of equations is consistent.