Solve the following systems by addition. 2x-y=1 and -2x+3y=5?

Answer 1

1st make 2x-1=y

substitude 2x-1=y into -2x+3y=5
-2x+3(2x-1)=5
-2x+6x-3-5=0
4x-8=0
4x=8
x=2
replace x=2 into 2x-y=1
2(2)-y-1=0
3-y=0
y=3

Answer 2

Your teacher probably wants to see something like this:

To do it by addition, write them one above the other:

2x - y = 1
+( -2x + 3y = 5)
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Now, add the terms as if you were doing long addition:

2x - 2x = 0; -y + 3y = 2y; 1 + 5 = 6.

This gives you:

0 + 2y = 6

Solving, y=3. Then, substituting y=3 in either of the given equations gives x = 2.

And, always check your work.

2(2) - 3 = 1 ?? Yes
-2(2) + 3(3) = 5 ?? Yes.

Answer 3

2x - y + -2x + 3y = 1 + 5 : add the equations
2y = 6 : simplify
y = 3 : divide by 2
2x - 3 = 1 : plug y value into first equation
2x = 4 : add 3 to both sides
x = 2 : divide by 2

-2(2) + 3(3) = 5 ?
-4 + 9 = 5 so it checks

Answer 4

2x-y=1
-2x+3y=5
2y=6
y=3
2x-3=1
2x=4
x=2

Answer 5

(3/2,2)