Answer:
Step-by-step explanation:
To solve the system of equations:
5
�
+
4
�
=
12
5x+4y=12
40
�
+
32
�
=
112
40x+32y=112
Let's first simplify the equations if possible:
Equation (1):
5
�
+
4
�
=
12
5x+4y=12
Equation (2):
40
�
+
32
�
=
112
40x+32y=112
Now, let's multiply Equation (1) by 8 to make the coefficients of
�
y the same:
Equation (1) becomes
40
�
+
32
�
=
96
40x+32y=96
Now, we have a system of equations with the same coefficient for
�
y:
40
�
+
32
�
=
96
40x+32y=96
40
�
+
32
�
=
112
40x+32y=112
Now, subtract Equation (1) from Equation (2):
(
40
�
+
32
�
)
−
(
40
�
+
32
�
)
=
112
−
96
(40x+32y)−(40x+32y)=112−96
This simplifies to
0
=
16
0=16, which is not possible.
Since the result is a contradiction, it means that the system of equations has no solution. In geometric terms, the two equations represent parallel lines that do not intersect.
