Question 122275: What would the coordinates be when solving this system by graphing?
2x + y = 4
x + y = 3
Found 2 solutions by praseenakos@yahoo.com, algebrapro18:
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! Question:
What would the coordinates be when solving this system by graphing?
2x + y = 4
x + y = 3
Answer:
Rewrite the equation in the form, y = mx +c
y = -2x +4
y = - x + 3
Now graph these equations....
Then the graph will come like this.....
From the graph you can see that.....two lines intersect at a point whose coordinate is (1,2)
Which is the solution.
Hope you found it useful.
Regards.
Praseena.
Answer by algebrapro18(249)  (Show Source):
You can put this solution on YOUR website! 2x + y = 4
x + y = 3
well first off we need to solve both equations for y, thus putting them into y = mx+b form.
y = -2x +4
y = -x + 3
from the equations we can get one set of points just by knowing that the b in y=mx+b is the y-intercept. We know that the first equation crosses the y-axis at (0,4) and the second equation crosses at (0,3). Now we need to find a second set of equations we can use to graph those lines and there are 2(really 3 but 3 good ones)methods for doing this.
Method one- setting both equations equal to zero and solving for x(finding the x-intercept)
-2x+4 = 0
-2x = -4
x = 2
-x + 3 =0
-x = -3
x = 3
so the first equation has an x-intercept at (2,0) and the second equation has an x-intercept at (3,0). Now we have 2 sets of points for each equation. Equation one goes though (0,4) and (2,0) and the second equation goes though (0,3) and (3,0). Now we can graph the lines and see where they intersect.
Method 2- using the slope
for this all you need to remember is that the slope(m) is rise/run or rYse/run if that will help you remember. The first equation has a slope of -2 so all you need to do is add -2 to the y value of the y intercept and 0 to the x value of the y intercept. The second equation has a slope of -1 so all you need to do is add -1 to the y value to the y intercept and the 0 to the x value to the y intercept.
(0+0,4-2) = (0,2)
(0+0, 3-1) = (0,2)
and now you have your points which are (0,4) and (0,2) for the first equation and (0,3) and (0, 2) for the second equation. To solve this by graphing you would plot those points and draw a line though each set and see where the two lines intersect.
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