Identify the solutions of the systems of equations, if any.
X+2y=7
3x-4y=6
A.(4,2/3)
B.(4,3/2)
C.(2/3,4)
D.(3/2,4)
Does any one knows the answer
Multiply top equation by 2.
2x + 4y = 14
3x - 4y = 6
Add the two equations.
5x = 20
Solve for x, then y.
To identify the solutions of the system of equations, we can solve them using the method of substitution or elimination. Let's use the method of elimination in this case.
First, let's multiply the first equation by 3 and the second equation by 2 to eliminate the variable x:
3(x + 2y) = 3(7) -> 3x + 6y = 21
2(3x - 4y) = 2(6) -> 6x - 8y = 12
Now, we have the following system of equations:
3x + 6y = 21
6x - 8y = 12
To eliminate the variable y, let's multiply the first equation by 2:
2(3x + 6y) = 2(21) -> 6x + 12y = 42
Now, we have the following system of equations:
6x + 12y = 42
6x - 8y = 12
To eliminate the variable x, let's subtract the second equation from the first equation:
(6x + 12y) - (6x - 8y) = 42 - 12 -> 20y = 30 -> y = 30/20 -> y = 3/2
Now, substitute the value of y back into one of the original equations (let's use the first equation):
x + 2(3/2) = 7 -> x + 3 = 7 -> x = 7 - 3 -> x = 4
Therefore, the solution to the system of equations is (4, 3/2), which corresponds to option B.