Solve the system 2x+y=2,3x+2y=5 algebraically:

(1) Method I; substitution:

Solve the first equation for y : 2x+y=2

Subtract 2x from each side to get y=-2x+2

Now substitute this expression for y into the second equation:

3x+2y=5

3x+2(-2x+2)=5 solve for x:

3x-4x+4=5

-x=1 ==> x=-1

**If x=-1 then y=-2(-1)+2=4**

**So the solution is x=-1,y=4 or the point (-1,4).**

Check: 2(-1)+4=2 and 3(-1)+2(4)=5.

(2) Method II; elimination:

2x+y=2

3x+2y=5 Choose to eliminate y; multiply the first equation by -2 :

-4x-2y=-4

3x+2y=5 Now add the two equations together:

x+0=-1 ==> x=-1 and proceed as above.

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The solution to the system is (-1,4)

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**Further Reading**

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