CHAPTER XVII.
Simultaneous Equations.
167. Consider the equation 2 x + 5 y = 23, which contains two unknown quantities.
From this we get y = {23-2x}{5} (1).
Now for every value we give to x there will be one corresponding value of y. Thus we shall be able to find as many pairs of values as we please which satisfy the given equation. Such an equation is called indeterminate.
For instance, if x = 1, then from (1) y = {21}{5}.
Again, if x =- 2, then y= {27}{5} and so on.
But if also we have a second equation of the same kind expressing a different relation between x and y, such as we have from this y = {23-8}{5}.
If now we seek values of x and y which satisfy both equations, the values of y in (1) and (2) must be identical.
Therefore {23-2x}{5} = {24-3x}{4}
Multiplying across, 92 - 8x = 120 - 15x ; 7x = 28; x = 4.
Substituting this value in equation (1), we have
y = {23-2x}{5} = {23-8}{5} = 3.
Thus, if both equations are to be satisfied by the same values of x and y, there is only one solution possible.
