More Final Exam Help, part 2

For Algebra Students:

3x - y = 1
2x + 4y = 3
Use substitution to solve this system of equations.
3x - y (+ y) = 1 (+ y) add y to both sides
3x = 1 + y
3x (- 1) = y + 1 (- 1) subtract one from both sides
3x - 1 = y
Substitute this for y in the other equation.
2x + 4(3x - 1) = 3
2x + 12x - 4 = 3 use Distributive property
14x -4 = 3 combine like terms
14x = 7 add four to both sides
x = 1/2 divide by 14
3(1/2) -y = 1 substitute 1/2 for x
3/2 - y = 1 multiply 3 times 1/2
- y = -1/2 subtract 3/2 from each side
y= 1/2 divide by -1
ANSWER: (1/2, 1/2)

x - 5y = 0 multiply this by 2
2x - 3y = 7
2(x- 5y) = 0 2x - 10y = 0
subtract 2x - 3y = 7
-7y = -7
divide by -7 y = 1

x - 5(1) = 0 substitute 1 for y
x - 5 = 0 multiply
x = 5 add five to both sides.
answer: (5, 1)