Part A:
System of equations is a set of two or more equations involving the same set of variables and having the same solution.
Part B:
A problem can be solved using system of twoequations if two quantities are involved and there is a value associated with each quantity.
A problem that can be solved using the system of equations is given below.
The total number of boys and girls in a class is 40. Each boys has $1 with him and each girl has $2. The total amount the students in the class have is $65. Find the number of boys and girls in the class.
The number of boys and girls in the class can be found by creating two equations and solving it.
Part C:
Given:
The selling price of a sign, s=$20.
The selling price of a towel, t=$7.5.
The total money earned by selling signs and towels, T=$250.
Let x be the number of signs and y be the number of towels.
So, the expression for total money earned by selling signs and towels is,
[tex]\begin{gathered} sx+sy=T \\ 20x+7.5y=250\text{ ---(1)} \end{gathered}[/tex]It is given that Lindsay sells as many Towels as signs.
So, we can write
[tex]\begin{gathered} y=2x \\ 2x-y=0\text{ -----(2)} \end{gathered}[/tex]So, we obtained two equations in x and y.
Multiply equation (2) by 10.
[tex]20x-10y=0\text{ ----(3)}[/tex]Subtract (3) from (1).
[tex]\begin{gathered} 20x+7.5y-20x+10y=250 \\ 17.5y=250 \\ y=\frac{250}{17.5} \\ =14.28 \end{gathered}[/tex]Putting y=14.28 in equation (1), we can find the value of x also.
Hence, the given problem can be solved using the system of equations.
