SOLUTION: I can't understand Which strategies could be used for solving the following system of equations? 2x + y = 4 x - y = 2 a. Graph both equations on the coordinate plane

Click here to see ALL problems on Systems-of-equations

Question 100179: I can't understand
Which strategies could be used for solving the following system of equations?
2x + y = 4
x - y = 2
a. Graph both equations on the coordinate plane and find the point of intersection.
b. Solve the first equation for y and then substitute that expression into the second equation.
c. Add the two equations together resulting in an equation with one variable.
d. a, b, and c are all correct
Found 2 solutions by josmiceli, Earlsdon:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
All three are correct. You're looking for the (x,y) coordinates
of the intersection of 2 straight lines. All these methods will find that intersection, for example,

Now substitute in the 2nd equation

Now substitute back in the 1st.

So, the 2 lines intersect at the point (2,0)

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Which strategy will work?
Which ones have you tried???
In fact, all of the listed strategies will work!
a) Let's do the graph and see how it works.
First, solve each equation for y.
1) 2x+y = 4 Subtract 2x from both sides.
1a) y = -2x+4 (Red line on the graph)
2) x-y = 2 Add y to both sides.
2a) x = y+2 Now subtract 2 from both sides.
x-2 = y or y = x-2 (Green line on the graph)
Now these can be graphed:

You can see that the two lines intersect at x = 2, and y = 0 so the solution is: (2, 0)
b) Solve the first equation for y:
2x+y = 4 Subtract 2x from both sides.
y = -2x+4 now substitute this into the 2nd equation:
x-y = 2 Substitute y = -2x+4
x-(-2x+4) = 2
x+2x-4 = 2 Add 4 to both sides.
3x = 6 Divide both sides by 3.
x = 2 Substitute this into the first eqation:
y = -2(2)+4
y = -4+4
y = 0
The solution is:
(2, 0)
Try c on your own and you will see that all three methods will work.