What is the common point of these two equations x plus 2y equals 6 x plus y equals 2?

Answer 1

You can solve with graphing, substitution, or elimination.

GRAPHING

If you have a TI-83 or TI-84 graphing calculator, you can plug in each equation to Y= (the small button farthest to the left below the screen). Hit "GRAPH" (the small button farthest to the right below the screen) and wait for the animation to finish. Then press 2ND (the blue button), then "TRACE" (the button to the left of the GRAPH button), then press 5 or scroll down to "5: intersect" and press ENTER. Hit ENTER 3 times, and it should give you an intersection point at (-2, 4).

SUBSTITUTION

If you don't have a graphing calculator/app at your disposal, then I would recommend using substitution to solve this problem, simply because it's the easiest way to solve for this particular problem.

x+2y=6

x+y=2 <--- Solve for y by subtracting x from both sides.

x+2y=6

y=-x+2 <---Plug in "-x+2" for y in the top equation.

x+2(-x+2)=6 <---Distribute the 2.

x-2x+4=6 <---Combine like terms.

-x=2

x=-2 <---Plug in -2 for x into either of the original equations to find y.

-2+2y=6

OR <---Both of these should give you y=4.

-2+y=2

ELIMINATION

If you're feeling particularly industrious today, then you can solve the system of equations by means of elimination.

x+2y=6

x+y=2 <---To get rid of the x, you can multiply either equation by -1.

x+2y=6

-x-y=-2 <---Add x's to x's, y's to y's, and #'s to #'s.

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y=4 <---Plug y into either of the original equations to find your x.

So basically, you end up with an intersection point at (-2, 4). At least, I hope that's what you meant by "common point".