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how do i determine if the point is a solution to the system

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(3,-4) y=2x+1 y=-2/3x-3

Mar 23rd, 2015

To determine if a point is a solution to a system, it must first be a point on both of the lines.  

First we should determine if the point (3, -4) lies on the first line by plugging the x value into the first equation.

y = 2*3 + 1

y = 6 + 1 

y = 7

Since this is not the y value of the point (-4), then this cannot be a solution to the system.

You could also check the second equation by the same procedure,

y = -2/3*3 - 3

y = -2 -3

y = -5

This is also not the point, therefore the point (3,-4) is not the solution to the system of equations.

Please let me know if you need any clarification of this explaination.

Mar 23rd, 2015

I still don't understabd 

Mar 23rd, 2015

What I showed you was a proof that the point given does not lie on either of the lines.  If the point is not on the line, then it cannot be the solution.  

A point that lies on the line would give you the y value back when you plugged in x.  For example, if you wanted to know if (1,6) is a solution to y = 2x +4.  We plug in x = 1

y = 2*1 + 4

y = 2 + 4

y = 6

Since 6 is also the value given by the point, it is a solution for the line.

Another way you could have solved the original problem, would be to solve the system of equations like any other and ignore the point.  If the solution you reach is the same as the point then you know that the point is the solution to the system of equations.

y=2x+1 y=-2/3x-3

Solve the system:

2x + 1 = -2/3x - 3

8/3x = - 4

x = -4*3/8

x = - 3/2

y = 2*-3/2 + 1

y = -3 + 1

y = -2

Solution to the system of equations is (-3/2 , -2) and not the point (3 , -4)

Mar 23rd, 2015

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