174. We add a few cases in which, before proceeding to
solve, it will be necessary to simplify the equations.
Ex.1. Solve 5(x + 2y)- (3x + 11y)=14 (1), 7x-9y-S(x-4y) = 38 (2).
From (1) 5x+10y-3x-11y = 14; 2x-y = 14 (3).
From (2) 7 x -9y - 3x + 12y = 38 ; 4x + 3y = 38 (4).
From (3) 6x-3y = 42; and hence we may find x = 8, and y =2.
Ex. 2. Solve 3x - {y-5}{7} = {4x-3}{2} {3y+4}{5} - {1}{3}(2x-5)=y (2).
Clear of fractions. Thus from (1) 42x-2y + 10 = 28x-21; 14x-2y =-31 (3).
From (2) 9y + 12 - 10x + 25 = 15y ; 10x + 6y = 37 (4).
Eliminating y from (3) and (4), we find that x = {14}{13} .
Eliminating x from (3) and (4) , we find that y = {207}{26}
Note. Sometimes, as in the present instance, the value of the second unknown is more easily found by elimination than by substituting the value of the unknown already found.
EXAMPLES XVII. b.
1. {2x}{3}+y-16, x + {y}{4} = 14 2. {x}{5} + {y}{2} = 5, x - y = 4 3. {5x}{6}-y=3, x - {5y}{6} = 8 4. x - y = 5, {x}{4} - {y}{5} = 2 5. {x}{9} + {y}{7} =10, {x}{3} + y = 50. 6. x = 3 y, {x}{3} + y = 34
