Find the solution to the system of equations by the substitu

Find the solution to the system of equations by the substitution method. Check your answer. Write solution in the form (p,q)

p + 2q - 4 = 0

7p - q - 3 = 0

Solution

We have the following system of linear equations:

p + 2q -4 = 0...(1) and 7p - q -3 = 0...(2).

From the 1st equation, we have p = 4 - 2q. On substituting this value of p in the 2nd equation, we have 7(4 - 2q) - q - 3 = 0 or, 28 - 14q - q - 3 = 0 or, 25 - 15q = 0 or, 15q = 25 so that q = 25/15 = 5/3. Now, p = 4 - 2q = 4 - 2*5/3 = 4 - 10/3 = 2/3. We can verify this result by substituting p = 2/3 and q = 5/3 in either of the 1st and the 2nd equations. On substitution in the 1st equation, we get 2/3 + 2(5/3) - 4 = 0 or, 2/3 + 10/3 - 4 = 0 or, 12/3 - 4 = 0 or 4 - 4 = 0 which is correct. On substitution in the 2nd equation, we get 7((2/3) - 5/3 - 3 = 0 or, 14/3 - 5/3 - 3 = 0 or, 9/3 - 3 = 0 or 3 - 3 = 0 which is correct. Thus the solution is (p,q) = ( 2/3. 5/3)