Answer:
The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).
Step-by-step explanation:
To see if the answer to an equation is right, you just have to put the value of X and Y into the equation system, since we don´t have the equation system that the student used, we will make our own, so we will start by stating that Notebooks are represented by X and index cards are represented by Y.
Your equation would look like this:
3x+ 4y=34
The student said that the price of the notebook is $5 and the index card would be $1, now we put those values into the equation.
3(5)+4(1)=32
15+4=32
19=32
Since 19 is not equal to 32, the equation is wrong, therefore the student is wrong.
Now to solve it you get your other equation, since if he had bought 5 and 5 he would have needed 18 extra dollars that means that
5x+5y= 32 +18
5x+5y=50
With the two equations you just use elimination process to create a single equation:
(5x+5y=50)-3= -15x-15y=-150
(3x+4y=32)5 = 15x+20y= 160
You eliminate the x from the equation and are left with:
-15y+20y= -150+160
5y=10
y=[tex]\frac{10}{2}[/tex]
y=2
Now that you have the value of Y you just put it into the equation to know the value of x:
5x + 5(2) = 50
5x+10=50
You clear the x and the result would look like this:
x= [tex]\frac{50-10}{8}[/tex]
x=8
