Let's solve the system of equations:
1) 3x + 2y = 7
2) -3x - 2y = (box)
Choosing a number in the box:
If we pick any number that is not equal to 7, we will find that the system of equations has a unique solution.
Let's choose the number 6 in the box.
Substituting the value into equation 2:
-3x - 2y = 6
Now, we can add equation 1 and equation 2:
(3x + 2y) + (-3x - 2y) = 7 + 6
0x + 0y = 13
0 = 13
This equation is not true, which means the system of equations is inconsistent. Therefore, the system of equations has no solution.
Different number in the box:
If we pick the number 7 in the box, we can see that the system of equations becomes:
-3x - 2y = 7
Adding equation 1 and equation 2:
(3x + 2y) + (-3x - 2y) = 7 + 7
0x + 0y = 14
0 = 14
Again, this equation is not true, meaning the system of equations is inconsistent. Therefore, the system of equations has no solution.
In both cases, we find that the system of equations has no solution.
solve the following system of equations with your choice of number in the box.
3x+2y=7
-3x-2y= (box)
how many solutions did you find?
pick a different number in the box that results in a different number of solutions
1 answer
1 answer