Question 1180577
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Find the constant m for which all three lines 2x - y - 4 = 0 , x + 2y + 3 = 0 and mx + y - 1 = 0 intersect at one point.
Note: Can you please show your full solution? Thank you!
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<pre>

First, solve the system to find the coordinates of the intersection point.


    2x - y =  4    (1)

    x + 2y = -3    (2)


I will solve by the Substitution method.

From equation (1), express  y = 2x - 4 and substitute this expression into equation (2)


    x + 2*(2x-4) = -3

    x + 4x - 8 = -3

        5x     = -3 + 8 = 5

         x              = 5/5 = 1


Then y = 2x-4 = 2*1 - 4 = 2 - 4 = -2.


Thus the solution to the system is  (x,y) = (1,-2);  so, the intersection point is (1,-2).


    
    Ok, we just solved half of the problem.

    Now our goal is to find  "m"  in the last equation.



For it, substitute the found coordinates of the intersection point  x= 1,  y= -2  into the equation

    m*1 + (-2) -1 = 0,


which gives the <U>ANSWER</U>  m = 3.
</pre>

Solved, explained, and full solution is shown, step by step in all details.



Have a nice day (!)