Solve using the appropriate method.
0.05x+0.25y=66
0.15x+0.05y=72
I came up with the answer (420,180) Is this correct?
a)The solution is___?(simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair)
b)Infinitely many solutions
c)No solution
you are correct
as you surely verified, by using the values in the equations ???
To solve the system of equations:
0.05x + 0.25y = 66 ...(equation 1)
0.15x + 0.05y = 72 ...(equation 2)
There are a couple of methods to solve this system of equations, including substitution, elimination, or matrix methods.
Let's use the elimination method.
Step 1: Multiply both sides of equation 1 by 100 to eliminate the decimals:
5x + 25y = 6600 ...(equation 3)
Step 2: Multiply both sides of equation 2 by 100 to eliminate the decimals:
15x + 5y = 7200 ...(equation 4)
Step 3: Multiply equation 3 by -3 and equation 4 by 1 to create cancellation:
-15x - 75y = -19800 ...(equation 5)
15x + 5y = 7200 ...(equation 4)
Step 4: Add equation 5 and equation 4 together to eliminate variable x:
(-15x + 15x) + (-75y + 5y) = -19800 + 7200
0 + (-70y) = -12600
-70y = -12600
Step 5: Solve for y:
y = -12600 / -70
y = 180
Step 6: Substitute the value of y in any one of the original equations, such as equation 1:
0.05x + 0.25(180) = 66
0.05x + 45 = 66
0.05x = 66 - 45
0.05x = 21
x = 21 / 0.05
x = 420
Therefore, the solution to the system of equations is (420, 180).
The answer you came up with (420, 180) is correct.