Name: Keisha
Secondary
Student
I need to solve this problem by using the substitution method.
3x+y=1
x=2y+5
Please help me understand the method to solve.
I also have the following
question as well:
Need to translate to a system of equation and solve; A collection of
dimes and quarters total $3.55. There are 25 coins in all. How
many quarters are there?
Thanks in advance Keisha
Hi Keisha,
The substitution method means that you start with one of the equations, use it to solve for one of the variables in terms of the other, substitute into the other equation and then solve this equation. So let's try it with your first problem.
Select one of the equations and use it to solve for one of the variables in terms of the other:
I would select the second equation since it is already in the right form. That is it has one of the variables, x, in terms of the other, y.
x = 2y + 5
Substitute into the other equation
The other equation is 3x + y = 1, so substitute x = 2y + 5 into this equation
3x + y = 1 so
3(2y + 5) + y = 1
Solve this equation
Simplify and solve for y.
3(2y + 5) + y = 1 so
6y + 15 + y = 1
7y = -14
y = -2
You are almost done. You know y = -2 and you need to find x. Use the second equation you started with.
x = 2y + 5
x = 2(-2) + 5
x = 1
For the second problem I would think in terms of cents rather than dollars.
A collection of dimes and quarters total 355 cents. There are 25 coins in all. How many quarters are there?
Let the number of dimes be d and the number of quarters be q. There are 25 coins in all so
d + q = 25
Each dime is worth 10 cents so the value of the dimes is 10d cents. Each quarter is worth 25 cents so the value of the dimes in 25q cents.Hence
10d + 25q = 355
Now use the substitution method to find q.
Penny