Question 3.3: Given the simultaneous equations 2x + 3y = 0.75 (1) 5x + 2y ......

In these two equations, neither the x- nor the y-terms are the same. If equation (1) is multiplied by 2 and equation (2) is multiplied by –3, the y-terms in both equations will be the same with opposite signs. Then proceed as in Worked Example 3.1 above.

Step 1: Eliminate y-terms from the system of equations:

4x + 6y = 1.5             (1)× 2

\underline {−15x  −  6y = 18}    (2)×−3

−11x = −16.5           adding

x = \frac {−16.5}{−11}= 1.5        solving for x

Step 2: Solve for y by substituting x = 1.5 into either equation (1) or equation (2):

2(1.5) + 3y = 0.75        substituting x = 1.5 into equation (1)

3y = 0.75 − 3

y = \frac {−2.25}{3}

Step 3: Checking the solution: x = 1.5,    y = −\frac {2.25}{3} is left as an exercise for the reader.