Question #23931

The value of m for which 2x+3y=11 , y=mx+3 , 2x-4y=-24 has common solution is?

Expert's answer

Let's solve the system of the first and the third equations:

2x+3y=11, (1)

2x-4y=-24. (3)

Let's subtract (1) from (3):

(2x+3y) - (2x-4y) = 11 - (-24) ==>

2x+3y - 2x+4y = 11 + 24 ==>

7y = 35 ==> y = 35/7.

(1) ==> x = (11-3y)/2 = (11-3*35/7)/2 = -2.

Now let's substitute x = -2, y = 35/7 into y=mx+3:

35/7 = -2m + 3 ==> m = (3 - 35/7)/2 = -1.

Therefore, the value of m for which 2x+3y=11& ,& y=mx+3& ,& 2x-4y=-24 has common solution is m = -1.

2x+3y=11, (1)

2x-4y=-24. (3)

Let's subtract (1) from (3):

(2x+3y) - (2x-4y) = 11 - (-24) ==>

2x+3y - 2x+4y = 11 + 24 ==>

7y = 35 ==> y = 35/7.

(1) ==> x = (11-3y)/2 = (11-3*35/7)/2 = -2.

Now let's substitute x = -2, y = 35/7 into y=mx+3:

35/7 = -2m + 3 ==> m = (3 - 35/7)/2 = -1.

Therefore, the value of m for which 2x+3y=11& ,& y=mx+3& ,& 2x-4y=-24 has common solution is m = -1.

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