Question 390460: 2. X = 2-seat tables
y = 4-seat tables
2x + 4y = 56 (max)
x + y = 17
Solve for x and y that allows the maximum number of customers
2x + 2y = 34
2y = 22
y = 11
x = 6
2. Use the system of equations from number 1 and solve using the substitution method to determine how many of each type of table should be purchased. Explain or show work for all steps used to solve the problem.
I have problems with subsitutions can I please have help with the answer thank you
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 2x+4y=56_x+y=17
Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
2x+4y=56_x=-y+17
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -y+17.
2(-y+17)+4y=56_x=-y+17
Multiply 2 by each term inside the parentheses.
-2y+34+4y=56_x=-y+17
Since -2y and 4y are like terms, subtract 4y from -2y to get 2y.
2y+34=56_x=-y+17
Since 34 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 34 from both sides.
2y=-34+56_x=-y+17
Add 56 to -34 to get 22.
2y=22_x=-y+17
Divide each term in the equation by 2.
(2y)/(2)=(22)/(2)_x=-y+17
Simplify the left-hand side of the equation by canceling the common factors.
y=(22)/(2)_x=-y+17
Simplify the right-hand side of the equation by simplifying each term.
y=11_x=-y+17
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 11.
y=11_x=-(11)+17
Multiply -1 by the 11 inside the parentheses.
y=11_x=-11+17
Add 17 to -11 to get 6.
y=11_x=6
This is the solution to the system of equations.
y=11_x=6
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