Question

5x+3y=24,3x+5y=16 then x+y=?

Answer 1

Step-by-step explanation:

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Answer 2

If 5x + 3y = 24 and 3x + 5y = 16, then x + y is equal to 5.

Step-by-step Explanation

Given:

Two equations, $5x + 3y = 24$ and $3x + 5y = 16$

To be found:

To find the value of $x + y$

Solution:

Here, the method to be used is the elimination method.

We have two equations,

$5x + 3y = 24$   ---------------------(1), and

$3x + 5y = 16$   ---------------------(2)

Now, multiplying eq(1) by 3 and eq(2) by 5, we get

$15x+9y=72$  --------------------(3)

$15x+25y=80$ ---------------------(4)

Now, the coefficient of x in both eq(3) and eq(4) are equal.

Next, subtracting eq(3) from eq(4), we get

$15x+25y-(15x+9y)=80-72\\\implies 15x+25y-15x-9y=80-72\\\implies 15x-15x+25y-9y=8$

Removing the x terms, we get

$16y=8\\\implies y=\frac{8}{16}\\\implies y=\frac{1}{2}$

Now, putting the value of y in eq(2), we get

$5x+3(\frac{1}{2} )=24\\\implies5x=24-\frac{3}{2} \\\implies 5x=\frac{45}{2}$

So, we get the value of x as,

$x=\frac{45}{2 \times 5} \\\implies x=\frac{9}{2}$

Hence, by adding x and y, we get

$x+y=\frac{9}{2} +\frac{1}{2} \\\implies x+y=\frac{10}{2} \\\implies x+y=5$

Therefore, If 5x + 3y = 24 and 3x + 5y = 16, then  the value of x + y is 5.

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