SOLUTION: I have to solve the problem by using substitution Method. If the problem has no solution or an infinite solution or an answer. 1. x + 7Y = 16 -3X + 6Y= 33 2. X + Y = 1

Question 63519: I have to solve the problem by using substitution Method. If the problem has no solution or an infinite solution or an answer.
1. x + 7Y = 16
-3X + 6Y= 33
2. X + Y = 1
X + Y = 2
This problem has to be sloved by equations by any method.
8x + 9 = -5y
-3x + 3y = -21
In a recent game Will scored 42 points on a combination of 18 two and three point baskets. How many shots of each type were made?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve the problem by using substitution Method. If the problem has no solution or an infinite solution or an answer.
1.
1st: x + 7Y = 16
2nd: -3X + 6Y= 33
Solve 1st for x, as follows:
3rd: x=16-7y
Substitute into 2nd to solve for y as follows:
-3(16-7y)+6y=33
-48+21y+6y=33
27y=81
y=3
---------
Substitute in 3rd to solve for x, as follows:
x=16-7(3)
x=-5
Check answer in 2nd as follows:
-3(-5)+6(3)=33
15+18=33
33=33
========================

2.
1st: X + Y = 1
2nd: X + Y = 2
Solve 1st for x, as follows:
x=1-y
Substitute in 2nd to get:
(1-y)+y=2
1=2
This is a contradiction indicating
there is no solution to this system
of equations. It also means you would
get two parallel lines that do not meet
in a point if you were to graph these
two equations.
========================
This problem has to be sloved by equations by any method.
8x + 9 = -5y
-3x + 3y = -21
Hint:
Write both equations in the form ax+b=c
Multiply the 1st by 3 and the 2nd by 8
Then subtract the 1st from the 2nd.
Good luck.
--------------
In a recent game Will scored 42 points on a combination of 18 two and three point baskets. How many shots of each type were made?
Let # of 2-pt baskets be "x"; these are worth 2x points in the game.
The # of 3-pt baskets is "18-x" ; these are worth 3(18-x)=54-3x points.
EQUATION:
points + points = 42
2x+54-3x=42
-x=-12
x=12 (# of 2-point baskets)
18-x=6 (# of 3-point baskets)
Cheers,
Stan H.

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