Find the points of intersection of the lines 4x + 3y = 5 and x = 2y – 7.
Suppose the given two lines intersect at a point P(x1, y1). Then, (x1, y1) satisfies each of the given equations.
∴ 4x + 3y = 5
or 4x + 3y – 5 = 0 …(i)
and x = 2y – 7
or x – 2y + 7 = 0 …(ii)
Now, we find the point of intersection of eq. (i) and (ii)
Multiply the eq. (ii) by 4, we get
4x – 8y + 28 = 0 …(iii)
On subtracting eq. (iii) from (i), we get
4x – 8y + 28 – 4x – 3y + 5 = 0
⇒ -11y + 33 = 0
⇒ -11y = -33
Putting the value of y in eq. (i), we get
4x + 3(3) – 5 = 0
⇒ 4x + 9 – 5 = 0
⇒ 4x + 4 = 0
⇒ 4x = -4
⇒ x = -1
Hence, the point of intersection P(x1, y1) is (-1, 3)