Tell whether the system has one solution infinitely many solutions or no solution.
1.5x+2y=11
3x+6y=22
a. one solution
b. infinitely many solutions
c. no solution
Now you should be able to do this one with the methods I showed you.
In fact, just solve it.
23
To determine whether this system of equations has one solution, infinitely many solutions, or no solution, we can use the method of elimination or substitution.
Let's use the method of elimination:
1. Multiply both sides of the first equation by 3 to make the coefficients of x equal:
4.5x + 6y = 33
2. Subtract the second equation from the modified first equation:
(4.5x + 6y) - (3x + 6y) = 33 - 22
4.5x + 6y - 3x - 6y = 11
1.5x = 11
3. Divide both sides of the equation by 1.5:
x = 11 / 1.5
x = 7.33
Now, substitute the value of x into one of the original equations. Let's use the first equation:
1.5(7.33) + 2y = 11
10.99 + 2y = 11
2y = 11 - 10.99
2y = 0.01
y = 0.01 / 2
y = 0.005
So, the solution to the system of equations is x = 7.33 and y = 0.005.
Since there is a unique solution, the answer is:
a. one solution