Solve for a and b is 3a-b= 7  and 2a = 4b-5

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve for a and b using 3a - b = 7  and 2a = 4b - 5.

Now 3a - b = 7

=> b = 3a - 7

Substitute this in 2a = 4b - 5

=> 2a = 4(3a - 7) -5

=> 2a = 12a - 28 - 5

=> 2a - 12a = 33

=> 10a = 33

This gives a = 33/10

b = 3a - 7

=> b = 3*33/10 - 7

=> b = 29/ 10

So a = 33/10 and b = 29/10

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equations:

3a - b= 7 ..............(1)

2a = 4b - 5

==> 2a - 4b = -5 .............(2)

We have a system of two equations and two variables.

Then we will use the elimination method to solve.

We will multiply (1) by 4 and subtract (2).

==> 12a - 4b = 28

==> 2a - 4b = -5

==> 10a = 33

==> a= 33/10 = 3.3

==> a= 3.3

==> Now we will substitute into (1) to find b.

==> b = 3a - 7

==> b= 3(3.3) - 7 = 9.9 - 7 = 2.9

==> b= 2.9

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