Question

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Answer 1

Answer:

a = 20

b = 10

Or if in coordinate format, (20,10)

Step-by-step explanation:

$\left \{ {{4a-3b=50} \atop {5a-2b=80}} \right.$

Solve the system using elimination:

In elimination, you want to eliminate a term. I want to eliminate b, so what I would do is to get it the same coefficient (LCM)

• $\left \{ {4a - 3b=50} \atop {5a-2b=80}} \right.$
• $\left \{ {{8a-6b=100} \atop {15a-6b=240}} \right.$        <= Multiply the equations by 3 to find LCM
• $-7a = -140$                                                                                                           Remember, if the terms you want to eliminate have the same sign in front of them ( - or +), subtract the top equation from the bottom. If they are different signs, add the two equations.
• $a=20$

Now, plug in 20 for an into any of the original equations

• 4a - 3b = 50
• 4(20) - 3b = 50
• 80 - 3b = 50
• -3b = -30
• b = 10

The solution of the system is written as a coordinate, in alphabetical order. Since the variables are a and b, you write it as (a,b).

The solution is $\boxed{(20,10)}$

-Chetan K