To solve this system using the addition method, we need to add the two equations together in order to eliminate one of the variables.
First, we will add the two equations:
(x - 2.8y) + (-x + 3.9y) = 0.6 + (-2.8)
After simplifying, we get:
1.1y = -2.2
y = -2
Now, we can substitute y = -2 back into one of the original equations to solve for x:
x - 2.8(-2) = 0.6
x + 5.6 = 0.6
x = -5
Therefore, the solution to the system is (-5, -2).
The addition method is a good choice for solving this system because it allows us to eliminate one of the variables by adding the two equations together. This simplifies the system and makes it easier to find the value of the remaining variable.
If we wanted to solve for x first, the addition method would still be a good choice. We could first add the two equations together as before to eliminate x and find the value of y. Then, we could substitute the value of y back into one of the original equations to solve for x. The addition method is versatile and can be used for solving for either variable first.
Writing Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain.
x - 2.8y = 0.6
-X + 3.9y = - 2.8
The solution is ___. (Type an ordered pair)
3 answers
Swimming Pool On a certain hot summer's day, 328 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $623.00. How many children and how many adults swam at the public pool that day?
There were children at the public pool.
There were children at the public pool.
Let's represent the number of children as 'C' and the number of adults as 'A'.
We can create a system of two equations to represent the given information:
C + A = 328 (Total number of people)
1.75C + 2.25A = 623 (Total revenue from admission)
To solve the system using the addition method, we will first multiply the first equation by 1.75 and subtract it from the second equation to eliminate one of the variables:
1.75(C + A) = 1.75(328)
1.75C + 1.75A = 574
1.75C + 2.25A = 623
Now, subtract the first equation from the second equation:
2.25A - 1.75A = 623 - 574
0.5A = 49
A = 98
Now that we have found the number of adults (A = 98), we can substitute this back into the first equation to solve for the number of children:
C + 98 = 328
C = 328 - 98
C = 230
Therefore, there were 230 children and 98 adults at the public swimming pool that day.
We can create a system of two equations to represent the given information:
C + A = 328 (Total number of people)
1.75C + 2.25A = 623 (Total revenue from admission)
To solve the system using the addition method, we will first multiply the first equation by 1.75 and subtract it from the second equation to eliminate one of the variables:
1.75(C + A) = 1.75(328)
1.75C + 1.75A = 574
1.75C + 2.25A = 623
Now, subtract the first equation from the second equation:
2.25A - 1.75A = 623 - 574
0.5A = 49
A = 98
Now that we have found the number of adults (A = 98), we can substitute this back into the first equation to solve for the number of children:
C + 98 = 328
C = 328 - 98
C = 230
Therefore, there were 230 children and 98 adults at the public swimming pool that day.