Calculate the solution to these simultaneous equations using the elimination method: (1)(1)5𝑝+𝑞5p+q==1313 (2)(2)𝑝−𝑞p−q==55
Question
Calculate the solution to these simultaneous equations using the elimination method: (1)(1)5𝑝+𝑞5p+q==1313 (2)(2)𝑝−𝑞p−q==55
Solution
Sure, let's solve these equations step by step:
Given equations are:
- 5p + q = 13
- p - q = 5
Step 1: Add the two equations together. This will eliminate q.
(5p + q) + (p - q) = 13 + 5 6p = 18
Step 2: Solve for p by dividing both sides by 6.
p = 18 / 6 p = 3
Step 3: Substitute p = 3 into the second equation to solve for q.
3 - q = 5 -q = 5 - 3 -q = 2
Multiply both sides by -1 to solve for q.
q = -2
So, the solution to the system of equations is p = 3 and q = -2.
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