Algebra Practice Problem The Solution

The problem! Find the numbers for X and Y which satisfies the following simultaneous equations:- -5x + y = -2 (i) 5x + 4y = 17 (ii)

Method 1 - Substitution The strategy here is to make the problem easier. If there was only ONE variable in the equation then the problem is easier. But remember you need to know how to solve the easier problem

Solution -5x + y = -2 5x + 4y =17 Make x the subject of eqn (i) -5x +y -y = -2-y eqn (i) eqn (ii) “Undo” adding the y to -5x. Carry out same operation on RHS of equation

-5x + 0 = -2 -y -5x/-5 = (-2-y)/-5 1x = (2+y)/5 “Undo” the multiplying of x by the -5 using the INVERSE operation of multiply i.e. divide. Do this to both sides of the equation

So now that we have a value for x we can substitute it into eqn(ii) x = (2+y)/5 5((2+y)/5)+4y =17 This is an equation in one variable. We have REDUCED the problem

Solving the single variable equation! :-} 5((2+y)/5) +4y =17 2 + y + 4y = 17 2 + 5y = 17 5y + 2 -2 = 17 - 2 5y + 0 = 15 5y/5 = 15/5 1y = 3 y = 3 5 divide 5 = 1 Gather like TERMS Make y the subject of the equation “Undo” the operations that are carried out on y i.e. carry out INVERSE operations.

Back substitute y into eqn(i) -5x + (3) = -2 -5x + 3 - 3 = -2 -3 -5x + 0 = -5 -5x/-5 = -5/-5 1x = 1 x =1

State the solution x =1; y =3 or (x,y) = (1,3)

Check the solution Substitute the values (1,3) for (x,y) into eqns (i) and (ii) -5(1)+(3) = -2 eqn (i) 5(1) + 4(3) = 17 eqn (ii) EVALUATE the equations -5 + 3 = -2 true! 5 + 12 = 17 true!