If x and y are 2 real numbers such that 5x+4y=9 and 3x+2y=5, then what is 4x+3y?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have 5x + 4y = 9 and 3x + 2y = 5. We need to find 4x + 3y.

Here we don't need to find x and y. The required result can be obtained by adding 5x + 4y = 9 and 3x + 2y = 5

=> 5x + 4y + 3x + 2y = 9 + 5

=> 8x + 6y = 14

=> 2(4x + 3y) = 14

=> 4x + 3y = 14/2

=> 4x + 3y = 7

We get 4x + 3y = 7.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll have to solve the system of equations to determine x and y.

We'll apply elimination method. For this reason, we''ll multiply the 2nd equation by -2 and we'll add the resulting equation to the first one.

-2(3x+2y) = -2*5

We'll remove the brackets:

-6x - 4y = -10

We'll add the resulting equation to the 1st equation:

-6x - 4y + 5x + 4y = 9 - 10

We'll eliminate y and we'll combine like terms:

-x = -1

x = 1

We'll substitute x = 1 into the 1st equation:

5 + 4y = 9

4y = 9 - 5

4y = 4

y  =1

Now, we'll calculate 4x+3y:

4x+3y = 4*1 + 3*1 = 7

The result of the expression 4x+3y, for x = y = 1, is 4x+3y = 7.

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