Question

Determine the solution of the system. Show your work. Y = 5x – 9 Y = 2x + 6

Answer 1

The solution is (x, y) = (5, 16). My "work" is to make use of a graphing calculator.

_____

You can subtract the second equation from the first. This gives

... 0 = 3x -15

Then, divide by 3 and add 5.

... 0 = x - 5

... 5 = x

Substitute this value into either equation to find y.

... y = 2x +6

... y = 2·5 +6

... y = 16

The strategy to subtract the second equation from the first is based on the observation that both equations give expressions for y, and the x-coefficient in the first equation is the larger of the two x-coefficients. Thus, the subtraction we chose will eliminate y and give an x-term with a positive coefficient.

Answer 2

Both define y, so they are equivalent.

5x-9=2x+6
3x-9=6
3x=15
x=5

Then plug in x into any of the equations
y=2(5)+6
y=10+6
y=16

Final answer: (5,16)