Question 876364
you have two equation to work with.


let:


x = number of 2 point shots.
y = number of 3 point shots.
z = number of 1 point shots.


since the total number of baskets is equal to 45, this leads to the equation of:


x + y + z = 45


since the total points is equal to 80, this leads to the equation of:


2x + 3y + z = 80


you are given that the number of 2 point shots is 19 more than the number of 1 point shots.


since x equals the number of 2 point shots and z equals the number of 1 point shots, this leads to the equation of:


x = z + 19


solve this equation for z to get:


z = x - 19


you can now replace z with x - 19 in both of those equations.


the attached picture below shows the details of the equations and the processing that follows.


in that picture, the following occurs:


number 1 shows you the original equations.


number 2 shows you that x = z + 19 which becomes z = x - 19 when you solve for z.


number 3 shows you the original equations after you replaced z with x - 19.


number 4 shows you the result of combining like terms and adding 19 to both sides of each of those equations.  the equations in number 4 are the equations that need to be solved simultaneously.


number 5 shows you the result of multiplying both sides of the first equation by 3 and then subtracting the second equation from the modified first equation.  the result of this operation is that the y variables cancel out and you are left with an equation of 3x = 93.  solving for x gets you x = 31.


number 6 solves for z now that x is known by using the equation of z = x - 19.
that gets you z = 12


number 7 replaces x and z with their respective values in the first equation and then solves for y which is equal to 2.


you now have the values for all 3 variables.
you have:
x = 31
y = 2
z = 12


number 8 uses those values in the original equations to confirm the solution is good.  since 45 = 45 and 80 = 80 are both true equations, the confirmation has been made and your solution is confirmed as good.


<img src = "http://theo.x10hosting.com/2014/may2101.jpg" alt="$$$" </>