# The solution of x-2y=3 and 2x+y=6 is: A. (0,3) B. (3,0) C. (3,2) D. (2,3) E. None of the above.

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Another way of solving the system of equations is by Elimination method.

That is a method where we tend to eliminate one variable to solve for the

other variable first. It is sometimes called the addition method.

x -2y = 3 Equation 1

2x + y = 6 Equation 2

We will have to multiply one equation by a number so that when we add the two equation we eliminate one of the variables. Say , we want the y to be eliminated first. Since equation 1 has -2y then equation 2 must have 2y so that when we add we get 0.

That means we multiply equation 2 by 2 .

2(2x+y) = 2*6

4x + 2y = 12 --> equation 3

Add the equation 1 and equation 3 ,

x - 2y = 3

+ 4x + 2y = 12

Gives , 5x = 15

divide both sides by 5 to isolate x , so x = 3 .

To solve for the value of y we have to use the value of x that we just got.

We can use either of the original equations.

Say, equation 1 .

x - 2y = 3

(3) - 2y = 3

3 - 3 -2y = 3 - 3 subtract both sides by 3 to get rid of 3 on the left side .

-2y = 0

-2y/-2 = 0/-2 divide both sides by -2 to get rid of -2 on -2y.

y = 0

Thus, the solution to the system is ( 3,0).

The solution of the set of equations x-2y=3 and 2x+y=6 has to be determined. One way of doing this is to actually solve the given set of equations. This was explained in the previous question asked by you. Another way would be to just substitute the values given in the options and see which satisfies both the equations.

A. (0,3)

`0 - 2*3 = -6 != 3`

B. (3,0)

3 - 2*0 = 3

2*3 + 0 = 6

We don't need to evaluate the equations for the other values given as we have already arrived at the correct solution.

**The solution of the set of equations x-2y=3 and 2x+y=6 is (3,0)**

The answer is (3,0), it can be proved through the method of substitution.

x-2y=3 2x+y=6

2x+y=6

y=6-2x

Substituting the above value into the equation,

x-2(6-2x)=3

x-12+4x=3

5x=3+12

5x=15

x=15/5

**x=3**

Inserting the value above in the equation to find the value of y,

2x+y=6

2(3)+y=6

6+y=6

y=6-6

**y=0**

**Therefore, (3,0).**

I can also prove it by inserting the values of x and y into the equation:

**2x+y=6**

2(3)+(0)=6

6+0=6

6=6

Therefore proved.

It can also be inserted into the other formula,

**x-2y=3**

(3)-2(0)=3

3-0=3

3=3

Therefore proved.