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I don't understand what I'm doing wrong. I multiplied the top one by 2 and the bottom one by 5 and found 4/5 for k but shouldn't h NOT be 5/4? why is it not working?

I don t understand what I m doing wrong I multiplied the top one by 2 and the bottom one by 5 and found 4

Answer :

The value of k is 4/5 and h ≠ 5/2

The system of equations is given as 5x + 2y = h and 2x + ky = 1

Multiply the first equation by 2

2 * 5x + 2 * 2y = 2h

10x + 4y = 2h

Multiply the second equation by 5

5 * 2x + 5 * ky = 5

10x + 5ky = 5

So, the equivalent system of equations is as follows

10x + 4y = 2h

10x + 5ky = 5

Compare the relative postions in both equations

10x = 10x

5ky = 4y

2h = 5

Divide both sides of 5ky = 4y by 5y

k = 4y/5y

k = 4/5

Divide both sides of 2h = 5 by 2

h = 5/2

According to the question, we are to calculate the value of k

This is k = 4/5

Also, we are to calculate the value h will not be

This is h ≠ 5/2

If h = 5/2, the equation will have infinite many solutions.

This is because the two equations in the system will now be equivalent

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Rewritten by : Barada