solve the system by substitution
x+y=9000
.06x+.15y=1215
.06x+.15(x-9000)=1215
.06x+.15x-1350=1215
.21x-1350=1215
x-1350+1214.79
x+2564.79
don't look right? where did I go wrong
from the first: y = 9000-x , you had it backwards
so .06x + .15(9000-x) = 1215
.06x + 1350 - .15x = 1215
-.09x = -135
x = 1500
then y = 9000-1500 = 7500
You also lost the equal sign in your last 2 lines
It appears that you made a mistake in your calculation. Let's go through the steps again to find the error:
1. From the first equation, x + y = 9000.
2. From the second equation, 0.06x + 0.15y = 1215.
To solve the system by substitution, you substitute the value of one variable from one equation into the other equation. Let's solve for x in the first equation and then substitute it into the second equation:
1. Solve the first equation for x: x = 9000 - y.
2. Substitute the value of x in the second equation: 0.06(9000 - y) + 0.15y = 1215.
Now, let's simplify this equation:
0.06(9000 - y) + 0.15y = 1215
540 - 0.06y + 0.15y = 1215
0.09y = 675
y = 675 / 0.09
y = 7500
Now, substitute the value of y back into the first equation to find x:
x + 7500 = 9000
x = 9000 - 7500
x = 1500
So, the solution to the system of equations is x = 1500 and y = 7500.
The mistake you made was in the step x - 1350 + 1214.79. It seems like there was an error in adding the numbers. The correct addition would be: x - 1350 + 1214.79 = x - 1350 + 1214.79 = x - 1350 + 1214.79 = x - 135 + 1214.79 = x + 1079.79, not x + 2564.79.
Always double-check your calculations to ensure accuracy.