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The value of x is 8 less than 3 times the value of y. The sum of x and y is 12. Write the two equations that represent this situation and solve for x and y using substitution, elimination, or graphing.

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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
User PhilMacKay
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