Taking into account the definition of a system of linear equations, James sold 5 boxes of cookies and 2 chocolate bars.
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
In this case, a system of linear equations must be proposed taking into account that:
Yesterday, James sold $29 worth of cookies and chocolate at his store and he sold 7 items. Knowing that James sells cookies for $5 a box, and chocolate for $2 a bar, the system of equations to be solved is
[tex]\left \{ {{x+y=7} \atop {5x+2y=29}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Solving the variable "x" of the first equation, you obtain:
x= 7-y
Substituting this equation in the second you get:
5×(7-y) + 2y= 29
Solving:
5×7- 5×y + 2y= 29
35- 5y + 2y= 29
-5y + 2y= 29 - 35
-3y= -6
y= (-6)÷ (-3)
y= 2
Replacing in the expression x= 7-y, the value of "x" is calculated as:
x= 7-2
Solving:
x=5
Finally, James sold 5 boxes of cookies and 2 chocolate bars.
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