Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑏4b==𝑎+5a+5 (2)(2)𝑏−4𝑎b−4a==2020
Question
Calculate the solution to these simultaneous equations using the substitution method: (1)(1)4𝑏4b==𝑎+5a+5 (2)(2)𝑏−4𝑎b−4a==2020
Solution
Sure, let's solve these equations step by step:
- From equation (1), we can express a in terms of b: a = 4b - 5
- Substitute a = 4b - 5 into equation (2): b - 4(4b - 5) = 20
- Simplify the equation: b - 16b + 20 = 20
- Combine like terms: -15b + 20 = 20
- Subtract 20 from both sides: -15b = 0
- Divide both sides by -15: b = 0
- Substitute b = 0 into equation (1): 4*0 = a + 5
- Simplify the equation: 0 = a + 5
- Subtract 5 from both sides: a = -5
So, the solution to the system of equations is a = -5 and b = 0.
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