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Here are three systems of equations. Which method (graphing, substitution, elimination) would you choose to solve and why. Use each method only once.

System #1 System #2 System #3

2x + 3y = 12 y = 2x +1 x = 2y + 5
4x + 3y = 18 y =-3x -2 x + 3y = 25

System #1

2x + 3y = 12   and  4x + 3y = 18

I'd use elimination on this one; we subtract equations and the 3y disappears,

2x = 6

x = 3

3y = 18-4x = 18 - 4(3) = 18 = 12 = 6

y = 2

System #2

y = 2x +1  and  y =-3x -2

Here I'd use elimination; we have two things equal to y, we eliminate y by setting the right sides equal to each other,

2x + 1 = -3x - 2

5x = -3

x = -3/5

y = 2x+1 = -1/5

check y=-3x -2 = 9/5 - 10/5 = -1/5, good

System #3

x = 2y + 5  and x + 3y = 25

Here I'd use substitution.   The first equation is for x in terms of y; if we substitute it into the second equation we'll just have an equation in y.

(2y + 5) +3y = 25

5y + 5 =25

5y = 20

y = 4

x = 2y+5 = 13

8

step-by-step explanation:

this is a subtraction problem.

10 - 2 = 8