8s+ 12 = 16, 6s+ 9t = 12 solve by substitution
I think you have a typo and you should have 12t in the first equation
If so, then drwls made the following observation
http://www.jiskha.com/display.cgi?id=1282324238
8s+12=16............. equation 1
6s+9t=12............. equation 2
Multiply equation 1 by 3 and equation 2 by 4 and subtract.
+24s+36= +48
+24s+36t=+48
- - - (sign will change when sub)
.............
36-36t=0
t=1
put t=1 in equation 2
6s+9(1)=12
s=1/2
CHECK 6(1/2)+9(1)=12
12=12
LHS=RHS so your answer is correct
To solve the given system of equations using the method of substitution, we need to solve one of the equations for one variable and substitute that expression into the other equation. Let's solve the first equation for s:
8s + 12 = 16
First, subtract 12 from both sides:
8s = 16 - 12
Simplifying,
8s = 4
Now, divide both sides by 8 to isolate s:
s = 4/8
s = 1/2
Now that we have the value of s, we can substitute it into the second equation:
6s + 9t = 12
Replacing s with 1/2:
6(1/2) + 9t = 12
Simplifying,
3 + 9t = 12
Next, subtract 3 from both sides:
9t = 12 - 3
9t = 9
Finally, divide both sides by 9 to solve for t:
t = 9/9
t = 1
Therefore, the solution to the system of equations is s = 1/2 and t = 1.