Question

If (0, a) and (b, 0) are the solutions of the following linear equations. Find ‘a’ and ‘b’.
8x – y = 34

Answer 1

Hint: Solutions of any equation means that those points lie on the graph of the given equation. Two points are given to us. The question can be solved in two ways, either analytically or graphically. For analytical methods, we will find the x and y coordinates of the points and replace the x in the equation with x – coordinate of the point and y in the equation with y – coordinate of the point.

Complete step-by-step answer:
Thus, we will be able to find the value of a and b. For a graphical method, we will graph the given line equation and first find the point whose x – coordinate is 0 and then a point whose y – coordinate is zero. Thus, y – coordinate of the former point is a and x – coordinate of the later point is b.
First of all, we will solve this question by analytical method. It is given that points (0, a) and (b, 0) are solutions of the linear equation 8x – y = 34.
This means, (0, a) and (b, 0) lies on the line 8x – y = 34 and satisfies the equation of the line.
Thus, in point (0, a), x – coordinate is 0 and y – coordinate is a.
Thus, we will replace x with x – coordinate and y with y – coordinate.
 $ \Rightarrow $ 8(0) – a = 34
 $ \Rightarrow $ a = ─34
And in point (b, 0), x – coordinate is b and y – coordinate is 0.
 $ \Rightarrow $ 8(b) – 0 = 34
 $ \Rightarrow $ b = $ \dfrac{17}{4} $
Now, we will solve by graphical method.
First, we will graph the line 8x – y = 34. Then, we will find the points at which the line intersects x – axis and y – axis. Those points (0, a) and (b, 0).

As we can see, the points (0, a) and (b, 0) are (0, ─34) and (4.25, 0).
Thus, a = ─34 and b = $ \dfrac{17}{4} $ = 4.25

Note: Students can solve the question in any method that they find easier. Moreover, another method will be to find the equation of the line passing through (0, a) and (b, 0) and compare it with the given equation of line, as both the equations will be the same.