5x-7y=-14
7y-5x=14
what is the solution of the system of equations? ANSWER IS B???
A) A point
B)Infinitely many solutions
C) no solution
Is the system consistent ot inconsistent?
ANSWER IS CONSISTENT
Is the system dependent or independent?
ANSWER IS DEPENDENT???
Are my answers correct?
5X - 7Y = 14
-5X + 7Y = 14
M1 = -A/B -5/-7 = 5/7
M2 = -A/B = 5/7
The 2 Eq have equal slopes and do
not intersect. therefore, no solution.
Ans = C
The Eq are not the same line. They
are, therefore, INDEPENDENT and
INCONSISTENT.
To find the solutions of the system of equations, we can solve them simultaneously. Let's solve these equations:
Equation 1: 5x - 7y = -14
Equation 2: 7y - 5x = 14
To solve this system, we can use several methods such as substitution, elimination, or graphing. Let's use the elimination method here:
Multiply equation 1 by 7 and equation 2 by 5 to eliminate the "x" term:
7(5x - 7y) = 7(-14) becomes 35x - 49y = -98 [Multiply equation 1 by 7]
5(7y - 5x) = 5(14) becomes 35y - 25x = 70 [Multiply equation 2 by 5]
Now we have two equations:
35x - 49y = -98
-25x + 35y = 70
If we multiply equation 2 by -7, we can eliminate the "y" term:
-7(-25x + 35y) = -7(70) becomes 175x - 245y = -490 [Multiply equation 2 by -7]
Now we have two equations:
35x - 49y = -98
175x - 245y = -490
If we divide the second equation by 35, we get:
5x - 7y = -14
We can see that the two equations are identical, meaning they represent the same line. Thus, there are infinitely many solutions to the system of equations.
Therefore, the solution of the system is option B, Infinitely many solutions.
Now let's check the consistency and dependence of the system:
Consistency: Since there are infinitely many solutions, the system is consistent.
Therefore, the answer is consistent.
Dependence: Since the equations represent the same line, they are dependent on each other.
Therefore, the answer is dependent.
Based on your explanation, your answers are correct.