Hi, can someone pls give me an idea how to do this? Thanks!
Use substitution to solve the following system.
L+r+s=20
R=l+3
L+5r+10s=129
I have to solve for all the variables, and am really confused. Any help is greatly appreciated.
I would be confused too, if I had 5 variables but only 3 equations
Unless R =r and L = l
so rewriting it:
l+r+s=20
r=l+3
l+5r+10s=129
sub r = l+3 into the first:
l + l+3 + s = 20 ----> 2l + s = 17 **
sub r = l+3 into the last:
l + 5(l+3) + s = 129
6l + s = 114 ***
subtract ** from ***
4l = 97
l = 97/4
into r = l+3 = 97/4 + 3 = 109/4
into l+r+s=20
97/4 + 109/4 + s = 20
s = -63/2
To solve this system of equations using substitution, we can start by solving one of the equations for one variable and then substitute it into the other equations.
Step 1: Solve one equation for a variable.
Let's solve the second equation, R = L + 3, for L:
L = R - 3
Step 2: Substitute the expression found in Step 1 into the other equations.
Now, substitute the expression L = R - 3 into the first and third equations:
Equation 1: L + r + s = 20
(R - 3) + r + s = 20
R + r + s - 3 = 20
Equation 3: L + 5r + 10s = 129
(R - 3) + 5r + 10s = 129
R + 5r + 10s - 3 = 129
Step 3: Simplify and rearrange.
Now we can simplify and rearrange the resulting equations to solve for the remaining variables.
Equation 1: R + r + s = 23
Equation 2: R + 5r + 10s = 132
Step 4: Solve for the remaining variables.
Since we have two equations with two variables (R, r, and s), we can solve them simultaneously. To find the values of R, r, and s, we need to solve these equations algebraically. One way to do this is by using elimination or substitution again.
Let's use substitution to solve these equations:
Take Equation 1: R + r + s = 23
R = 23 - r - s
Substitute this value of R into Equation 2:
(23 - r - s) + 5r + 10s = 132
Simplify and rearrange this equation:
23 - r - s + 5r + 10s = 132
-4r + 9s = 109
Now we have a new equation with r and s. We can continue solving for the remaining variables by using any of the available methods, such as substitution or elimination.
Remember, this explanation provides the steps to solve the given system of equations using substitution. Solving the equations further for r, s, and R requires additional algebraic manipulation.