Question

Question 1 (i)
Solve the following pair of linear equations by the elimination method and the substitution method:
x + y =5 and 2x - 3y = 4

Answer 1

The given equations are
x + y = 5 and 2x - 3y = 4

Solution by elimination method:
x + y = 5 ... (i)
2x –3y = 4 ... (ii)
Multiplying equation (i) by (2), we get
2x + 2y = 10 ... (iii)
2x –3y = 4 ... (ii)
Subtracting equation (ii) from equation (iii), we get
5y = 6
$y=\frac{6}{5}$
Putting the value in equation (i), we get
$x=5-\frac{6}{5}=\frac{19}{5}$
Hence, $x=\frac{19}{5}$ and $y=\frac{6}{5}$

Solution by substitution method

x + y = 5 ... (i)
Subtracting y both side, we get
x = 5 - y ... (iv)
Putting the value of x in equation (ii) we get
2(5 - y) - 3y = 4
-5y = - 6
$y=\frac{-6}{-5}=\frac{6}{5}$
Putting the value of y in equation (iv) we get
$x=5-\frac{6}{5}$
$x=\frac{19}{5}$
Hence, $x=\frac{19}{5}$ and $y=\frac{6}{5}$