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