Directions:
Solve each system by whatever method you would like: by graphing or by using the equation method, substitution or elimination.
Problem 1)
System:- Line 1: y = 3x -2
- Line 2 : y = 2x + 5
answer
Use the algebraic equation method
First find the x value of the solution:
- 3x - 2 = 2x + 5
- -2x -2x
- x - 2 = 5
- x = 7
Now substitute x = 7 into one of the equations to find the y value
- y = 2(7) + 5 = 14 + 5 = 19
The answer is the point (7, 19)
Problem 2)
System:- Line 1: 2y = 5x + 12
- Line 2 : y = 5x - 4
answer
Use the substitution method
First substitute Line 2 into the "y" of line 1:
- 2(5x - 4) = 5x + 12
- 10x - 8 = 5x + 12
- +8 +8
- 10x = 5x +20
- -5x -5x
- 5x = 20
- x =4
Now substitute x = 4 into one of the equations to find the y value
- y = 5(4) - 4 = 16
The answer is the point (4, 16)
Problem 3)
System:- Line 1: y = -11x + 42
- Line 2 : y = 7x - 12
answer
This problem is a good candidate for the equation method
First set the two equations equal and solve for x:
- -11x + 42 = 7x - 12
- +11x +11x
- 42 = 18x - 12
- +12 +12
- 54 = 18x
- 3 = x
Now substitute x = 3 into one of the equations to find the y value
- y = 7(3) - 12 = 9
The answer is the point (3, 9)
