Calculate the solution to these simultaneous equations using the elimination method: (1)(1)𝑝+3𝑞p+3q==1414 (2)(2)4𝑝+3𝑞4p+3q==2929
Question
Calculate the solution to these simultaneous equations using the elimination method: (1)(1)𝑝+3𝑞p+3q==1414 (2)(2)4𝑝+3𝑞4p+3q==2929
Solution
Sure, let's solve these equations step by step:
Given equations are:
- p + 3q = 14
- 4p + 3q = 29
Step 1: Align the equations so that like terms are vertically aligned:
p + 3q = 14 4p + 3q = 29
Step 2: Subtract the first equation from the second to eliminate q:
(4p + 3q) - (p + 3q) = 29 - 14 3p = 15
Step 3: Solve for p:
p = 15 / 3 p = 5
Step 4: Substitute p = 5 into the first equation:
5 + 3q = 14 3q = 14 - 5 3q = 9
Step 5: Solve for q:
q = 9 / 3 q = 3
So, the solution to the system of equations is p = 5 and q = 3.
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