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What is the common point of these two equations x plus 2y equals 6 x plus y equals 2?
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".
What else can I help you with?
What is the common point of these equations x plus 2y equals 6 x plus y equals 2?
When x = -2 then y = 4 which is the common point of intersection of the two equations.
What is the common point of these equations x equals 2 y equals 2x plus 1?
If X equals 2, then y = 5
What is the common point of these equations x plus 2y equals 6 and x plus y equals 2?
x = -2 and y = 4 (-2,4)
What kind of line is this equation 2y plus 4 equals 10 y equals -2x plus 5?
There are two equations in the question, not one. They are the equations of intersected lines, and their point of intersection is their common solution.
What is the common point of these equations x plus y equals 10 and x - y equals 6?
16
What is the common point of these equations x plus 2y equals 6 x plus y equals 2?
When x = -2 then y = 4 which is the common point of intersection of the two equations.
What is the common point of these equations x equals 2 y equals 2x plus 1?
If X equals 2, then y = 5
What is the common point of these equations x plus 2y equals 6 and x plus y equals 2?
x = -2 and y = 4 (-2,4)
What kind of line is this equation 2y plus 4 equals 10 y equals -2x plus 5?
There are two equations in the question, not one. They are the equations of intersected lines, and their point of intersection is their common solution.
What is the common point of these equations x plusy equals 6 x plus y equals 2?
x + y = 6x + y = 2These two equations have no common point (solution).If we graph both equations, we'll find that each one is a straight line.The lines are parallel, and have no intersection point.
What is the common point of these equations 2x plus 3y equals 12m and x - 3y equals -3?
It is [4m-1, (4m-2)/3]
What is the common point of these equations x plus y equals 10 and x - y equals 6?
16
What is the common point of these equations 2x plus 3y equals 12 x-3y equals -3?
x = 3 and y = 2 so the lines intersect at the point (3, 2)
What is the common point of these equations 2x plus 3y equals 12 and x - 3y equals -3?
(3, 2) because x = 3 and y = 2
What is the common point of these equations x plus y equals 10 x-y equals 6?
16
How many solutions does -x plus y equals -7 -x plus y equals 1 have?
-6
How many solutions does 2x plus y equals 5 and 2x plus y equals 4 have?
None. When these two equations are graphed, the two lines are parallel. Since they never intersect, there is no point that satisfies both equations.
