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Two straight lines have equations y = px + 4 and py = qx - 7 where p and q are constants. The two lines meet at the point (3,1). What is the value of q?

Sagot :

Given:

Equations of two lines are

[tex]y=px+4[/tex]

[tex]py=qx-7[/tex]

where, p and q are constants.

The two lines meet at the point (3,1).

To find:

The value of q.

Solution:

We have,

[tex]y=px+4[/tex]           ...(i)

[tex]py=qx-7[/tex]          ...(ii)

The two lines meet at the point (3,1). It means both equations must be satisfied by the point (3,1).

Putting x=3 and y=1 in (i), we get

[tex]1=p(3)+4[/tex]

[tex]1-4=3p[/tex]

[tex]\dfrac{-3}{3}=p[/tex]

[tex]-1=p[/tex]

The value of p is -1.

Now, putting p=-1, x=3 and y=1 in (ii), we get

[tex](-1)(1)=q(3)-7[/tex]

[tex]-1+7=3q[/tex]

[tex]\dfrac{6}{3}=q[/tex]

[tex]2=q[/tex]

Therefore, the value of q is 2.

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