A system of equations 3x - y = 7 and x - 2y = 4 is set up to determine the number of nickels and the number of quarters that Elissa has. Which ordered pair does not represent a valid solution to this system?
a. (2,-1)
b. (3,2)
Answer;
(3,2) is not a valid solution to the system
Explanation;
Given
3x - y = 7
x - 2y = 4
To get the ordered pair that represent a valid solution, we have to substitute the values of x and y in the above function.
For (2,-1)
The test goes thus;.
By substituton; 3x - y = 7 becomes
3(2) - -1 = 7
6 + 1 = 7
7 = 7
By substituton; x - 2y = 4 becomes
2 - 2(-1) = 4
2 + 2 = 4
4 = 4
So, (2,-1) is a valid solution.
We perform the same test on the second option.
For (3,2)
The test goes thus;.
By substituton; 3x - y = 7 becomes
3(3) - 2 = 7
9 - 2 = 7
7 = 7
By substituton; x - 2y = 4 becomes
3 - 2(2) = 4
3 - 4 = 4
-1 ≠ 4
So, (3,2) is not a valid solution.