Question

Given 4a+3b=65 and a+2b=35 solve by eliminating method

Answer 1

The solution of the system of equations is: a = $25/17$and b = $55/17$

The elimination method is a way to solve a system of linear equations by eliminating one of the variables by adding or subtracting the equations.

The goal is to get one of the variables to cancel out, leaving an equation in one variable that can be easily solved.

Given the system of equations:

$4a + 3b = 65$

$a + 2b = 35$

To eliminate one of the variables, we can multiply the first equation by -1 and add it to the second equation:

$(4a + 3b = 65) - (-1)(a + 2b = 35)$

This gives us:

3a + 5b = 30

Now we can solve for the variable that we didn't eliminate.

3a + 5b = 30

3a = 30 - 5b

a = (30 - 5b) / 3

Now we know that the value of "a" is $(30 - 5b) / 3$, we can substitute it in the first equation:

4a + 3b = 65

$4((30 - 5b) / 3) + 3b = 65$

$120 - 20b + 3b = 65$

120 - 17b = 65

-17b = -55

b = 55/17

Now we have the value of "b" we can substitute it in any of the equations to find "a"

a + 2b = 35

$a + 2(55/17) = 35$

$a = 35 - 2(55/17)$

$a = 35 - 110/17$

$a = 35 - 10/17$

So, the solution of the system of equations is:

a = 25/17 and b = 55/17

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brainly.in/question/16766451

brainly.in/question/4211888

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