Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑡4t==𝑟+5r+5 (2)(2)𝑡−4𝑟t−4r==2020
Question
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑡4t==𝑟+5r+5 (2)(2)𝑡−4𝑟t−4r==2020
Solution
Sure, let's solve these equations step by step.
First, let's rewrite the first equation to express r in terms of t:
4t = r + 5
Subtract 5 from both sides to isolate r:
r = 4t - 5
Now, let's substitute r in the second equation with 4t - 5:
t - 4(4t - 5) = 20
Simplify the equation:
t - 16t + 20 = 20
Combine like terms:
-15t + 20 = 20
Subtract 20 from both sides:
-15t = 0
Divide by -15:
t = 0
Now, substitute t = 0 into the first equation to find r:
4(0) = r + 5
Solve for r:
r = -5
So, the solution to the system of equations is t = 0 and r = -5.
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