Answer:
The given system
Explanations:
Given the system of equations as shown:
1.5x - 1.5y = 10.5____________ 1
4.5.x - 4.5y = 31.5 ___________2
Multiply equations 1 and 2 through by 10
15x - 15y = 105 _________________3 * 3
45x - 45y = 315 _________________4
Multiply equation 3 by 3 and subtract from equation 4
45x - 45y = 315 _________________3
45x - 45y = 315 _________________4
Since both expressions are the same, we can solve just one of the equations as shown;
45x - 45y = 315
Divide through by 45
x - y = 7
Let x = t where "t" is any real number
-y = -x + 7
y = x - 7
Substitute x = t into the expression for y to have;
y = t - 7
Hence the solution to the system of equations is (t, t-7)
Since the value of "t" can be any real number, hence the system of equations of an infinite number of solutions