Hello! I need help with these math questions, thanks! :)
1.) Solve the system by substitution.
5x + 2y = -17
x = 3y
2.) Solve the system by substitution.
x/3 + y = 4/3
-x + 2y = 11
3.) Solve the system by elimination.
2x - 3y = 0
2x + 6y = 3
4.) Solve the system by elimination.
3x - 5y =11
2x - 6y = 2
5x + 2y = -17
x = 3y
5(3y) + 2y = -17
15y + 2y = -17
17y = -17
y = -1
x = 3(-1)
x = -3
(-3, -1)
2.) Solve the system by substitution.
x/3 + y = 4/3
-x + 2y = 11
y = -x/3 + 4/3
-x + 2(-x/3 + 4/3) = 11
-x -2x/3 + 8/3 = 11
-5x/3 = =25/3
-3/5(-5x/3) = 25/3(-3/5)
x = -5
(-5, 3)
3.) Solve the system by elimination.
2x - 3y = 0
2x + 6y = 3
4x -6y =0
2x +6y = 3
6x = 3
x = 1/2
y = 1/3
(1/2, 1/3)
4.) Solve the system by elimination.
3x - 5y =11
2x - 6y = 2
6x -10x = 22
-6x + 18y = -6
8y = 16
y = 2
x = 7
(7,2)
easy as pie peeps
Hello I need help with word problem.
Coffee shop sells small and large coffee in one day they sell 508 cups of coffee. IF they sell 3 times as many large cups of coffee as small cups of coffee, How many of each size coffee's does the shop sell in a day?
127 small cups and 381 large cups.
Hello! I'd be happy to help you with your math questions. Let's start by solving each system of equations step by step.
1.) Solve the system by substitution.
To solve the system by substitution, we can substitute the value of x from the second equation into the first equation.
Given:
5x + 2y = -17 ---> Equation (1)
x = 3y ---> Equation (2)
Substituting the value of x from Equation (2) into Equation (1), we get:
5(3y) + 2y = -17
15y + 2y = -17
17y = -17
y = -1
Now, substitute the value of y into Equation (2) to find x:
x = 3(-1)
x = -3
Therefore, the solution to the system is x = -3 and y = -1.
2.) Solve the system by substitution.
To solve the system by substitution, we can substitute the value of x from the first equation into the second equation.
Given:
x/3 + y = 4/3 ---> Equation (1)
-x + 2y = 11 ---> Equation (2)
Solving Equation (1) for x:
x = 4 - 3y
Substituting the value of x from Equation (1) into Equation (2), we get:
-(4 - 3y) + 2y = 11
-4 + 3y + 2y = 11
5y = 15
y = 3
Now, substitute the value of y into Equation (1) to find x:
x/3 + 3 = 4/3
x/3 = 4/3 - 3
x/3 = 4/3 - 9/3
x/3 = -5/3
x = -5
Therefore, the solution to the system is x = -5 and y = 3.
3.) Solve the system by elimination.
To solve the system by elimination, we can add or subtract the equations so that one of the variables cancels out.
Given:
2x - 3y = 0 ---> Equation (1)
2x + 6y = 3 ---> Equation (2)
If we subtract Equation (1) from Equation (2), we get:
(2x + 6y) - (2x - 3y) = 3 - 0
2x + 6y - 2x + 3y = 3
9y = 3
y = 3/9
y = 1/3
Now, substitute the value of y into Equation (1) to find x:
2x - 3(1/3) = 0
2x - 1 = 0
2x = 1
x = 1/2
Therefore, the solution to the system is x = 1/2 and y = 1/3.
4.) Solve the system by elimination.
To solve the system by elimination, we can add or subtract the equations so that one of the variables cancels out.
Given:
3x - 5y = 11 ---> Equation (1)
2x - 6y = 2 ---> Equation (2)
If we multiply Equation (1) by 2 and Equation (2) by 3, we get:
6x - 10y = 22 ---> Equation (3)
6x - 18y = 6 ---> Equation (4)
If we subtract Equation (4) from Equation (3), we get:
(6x - 10y) - (6x - 18y) = 22 - 6
6x - 10y - 6x + 18y = 16y = 16
16y = 16
y = 1
Now, substitute the value of y into Equation (1) to find x:
3x - 5(1) = 11
3x - 5 = 11
3x = 16
x = 16/3
Therefore, the solution to the system is x = 16/3 and y = 1.
I hope this helps! Let me know if you have any further questions.