the best method for solving # 1 is substitution
x - 0.9y = 4.5......x = 0.9y + 4.5
now sub 0.9y + 4.5 in for x in the other equation
1.5(0.9y + 4.5) - 1.9y = -29 ----distribute through the parenthesis
1.35y + 6.75 - 1.9y = -29
1.35y - 1.9y = -29 - 6.75
-0.55y = -35.75
y = -35.75 / -0.55
y = 65
x - 0.9y = 4.5
x - 0.9(65) = 4.5
x - 58.5 = 4.5
x = 4.5 + 58.5
x = 63
solution is (63,65)
The best method for solving # 4 is by elimination
14x + 7y = 217
14x + 3y = 189...multiply by -1
-----------------
14x + 7y = 217
-14x - 3y = -189 (result of multiplying by -1)
----------------add
4y = 28
y = 28/4
y = 7
14x + 7y = 217
14x + 7(7) = 217
14x + 49 = 217
14x = 217 - 49
14x = 168
x = 168/14
x = 12
solution is (12,7)