“y” variable equal to 2y
1. Tina Thompson scored 34 points in a recent basketball game without
making any 3-point shots. She scored 23 times, making several free
throws worth 1 point each and several field goals worth two points each.
How many free throws did she make? How many 2-point field goals
did she make?
Let “x” equal the number of free throws made. Since x= free throws, they are worth 1 point each. and let “y” equal the number of field goals made, Since y=field goals, they are worth 2 point each.
Your first formula should look like this: 1x + 2y = 34. Your second formula should look like this: x + y = 23.
The first step is to decide which method you will use to solve this equation. Use the addition method.
First you must make one of the variables equal the same. Let’s make “y” equal the same.
Since both “y” variables need to be the same you must multiply both “y” variables by a number that will make them the opposite so therefore they will cancel out. In this equation you will multiply x + y = 23 by positive 2, and you will multiply 1x + 2y = 34 by a negative 1.
First equation. 1x + 2y = 34
1x(-1) + 2y(-1) = 34(-1) simplify.
-1x -2y = -34
In the second equation you must make the “y” variable equal to 2y so that it will cancel out the “y” value making it = 0. So you will multiply the equation by a positive 2.
Second Equation. x + y = 23
x(2) + y(2) = 23(2) Simplify.
2x + 2y = 46
Now you will simply add both equations together to create one equation like so.
-x – 2y = -34
+2x + 2y = 46
X = 12
Since “x” equals 12 you will now choose either of the original equations to plug “x” into and solve for “y”. In this case we will use the first equation. x +2 y = 34. Now plug in “ x = 12 ” and solve for “y”.
x + 2y =34
12 + 2y = 34 subtract 12 from each side to get Y by itself.
-12 + 12 +2 y = 34 – 12 Simplify.
2y = 22 Now you must divide both sides by 2 so that you can get Y by itself.
2y = 22
2 = 2
y = 11
So there for x = 12 and y = 11. Now to check your answer you simply plug the value of “x” and “y” into both of the original equations. Verifying they are correct.
x + 2y = 34
12 + 2(11) = 34
12 + 22 = 23
34 = 34 Correct.
x + y = 23
12 + 11 = 23
23 = 23 Correct
Since the “x” variable represented the number of free throws made, Tina Thompson made a total of 12 free throws. Since “y” variable represented the number of field goals made, she made a total of 11 field goals. Therefore Tina made 11 free throws and 12 field goals giving her a total of 34 points.
2. Let x be the cost of pizza
Let y be the cost of sodas
8 slices of pizza plus 4 sodas cost 36.12
6 slices of pizza plus 6 sodas cost 31.74
Use elimination to solve
8x + 4y = 36.12
6x + 6y = 31.74
-6 | 8x + 4y = 36.12
8 | 6x + 6y = 31.74
-48x – 24y = -216.72
48x + 48y = 253.92
24y = 37.2
y= 1.55
8x + 4(1.55) = 36.12
8x + 6.2 = 36.12
8x = 29.92
x = 3.74
slice of pizza cost 3.74
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