2x-4y=7; (6,1) Tell whether each point is a solution to the equation

Question

Graphing two variable equations

Answer 1

This can be done graphically and algebraically.

 

Algebraically, we know that the point they have given us (6,1) corresponds to a point on the coordinate system of (x,y). So, what they have given us is that x = 6 and y = 1.

 

To determine if the point is a solution, all you have to do is to plug the values into the equation:

 

2x - 4y = 7

2(6) - 4(1) = 7

12 - 4 = 7

8 = 7  Obviously, 8 does not equal 7, so we can see that the point is not a solution.

 

Graphically, we can show the same thing. For starters, we need to rearrange the equation to get it into point-slope form so it can easily be graphed.

 

2x-4y=7

-4y = 7-2x

y= 1/2(x) -7

 

Now you can see easily that the equation is a line of slope 1/2 which crosses the y axis at y=-7. If you graph such a line, you will clearly see that the point does not lie on it. You can also substitute the value of 6 for x into the equation. If the point lies on the line, then the value of y at x = 6 should be 1

 

y=1/2(6) - 7

y=3 -7

y= -4

 

I hope this helps!