We can represent this situation with two equations:
Equation 1: x = 3y - 8 (x is 8 less than 3 times y)
Equation 2: x + y = 12 (the sum of x and y is 12)
To solve for x and y, we can use substitution or elimination:
Substitution method:
Solve Equation 1 for x: x = 3y - 8
Substitute x = 3y - 8 into Equation 2: 3y - 8 + y = 12
Simplify and solve for y: 4y - 8 = 12
Add 8 to both sides: 4y = 20
Divide both sides by 4: y = 5
Substitute y = 5 into Equation 1: x = 3(5) - 8 = 7
Therefore, the solution is x = 7 and y = 5.
Elimination method:
Multiply Equation 2 by -1: -x - y = -12
Add Equation 1 and the new Equation 2: 2y - 8 = 0
Solve for y: 2y = 8
Divide both sides by 2: y = 4
Substitute y = 4 into Equation 2: x + 4 = 12
Solve for x: x = 8
Therefore, the solution is x = 8 and y = 4.
Graphing method:
Graph the two equations on the same coordinate plane.
The point where the two lines intersect is the solution.
The intersection point is (7, 5), which means x = 7 and y = 5.
Therefore, regardless of the method used, the solution is x = 7 and y = 5