Henry takes guitar and piano lessons. Last month, he went to 3 guitar lessons and 4 piano lessons for a total cost of $195. This month Henry went to 4 guitar lessons and 2 piano lessons for a total cost of $160.
The following system of equations can be used to determine the cost of each type of lesson.
The cost of each guitar lesson is represented by x. The cost of each piano lesson is represented by y. How much is a guitar lesson?
This is a system of (linear) equations problem. We can solve it by using either the substitution of elimination method. Looking at the two equation, we notice that if we multiply all the terms by negative two and add the equations we would eliminate the y variable. This would be the elimination method, because the equation now only contains the x variable it is a straightforward matter to solve for x.
The other method would be the elimination method. looking at the second equation, we see that all the terms are even so we can divide them all by two. This results in the equation 2x + y + 80. Subtracting 2x from each side yields y = 80 - 2x. Now we can substitute the value 80 - 2x in for y in the first equation and solve for x.
Either of the above methods will work, it is your preference to use whichever you decide is easier and more straightforward.
