# Simultaneous equations: how to solve these with the elimination method.2x+3y=7 and x-3y=2 4x-2y=7 and x-2y=1

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1. 2x+3y=7 and x-3y=2

Let, 2x+3y=7 ...(1)

x-3y=2 ... (2)

To eliminate y, we use the addition method of elimination.

Joining both equations, we get:

2x+3y+x-3y=7+2

2x+x+3y-3y=9

3x=9

x=9/3

**x=3**

To fine value of y, we put value of x in equation (1):

2(3)+3y=7

6+3y=7

3y=7-6

3y=1

**y=1/3**

**Therefore, x=3 and y=1/3**

2. 4x-2y=7 and x-2y=1

Let, 4x-2y=7 be equation 1

and x-2y=1 be equation 2

To eliminate y we use subtraction method of elimination:

4x-2y-x+2y=7-1

4x-x-2y+2y=6

3x=6

x=6/3

**x=2**

Putting value of x in eq. 1:

4(2)-2y=7

8-2y=7

-2y=7-8

-2y=-1

y=-1/-2

**y=1/2**

**Therefore, x=2 and y=1/2.**

(1) 2x + 3y = 7

(2) x - 3y = 2

(1) + (2)

3x = 9 (This is what is meant by elimination since we have eliminated a variable.)

Now its single variable and can be solved for x. Plug this into eq (2) and solve for y.

(1) 4x - 2y = 7

(2) x - 2y = 1

(1) - (2)

3x = 6 (This is what is meant by elimination since we have eliminated a variable.)

Now its single variable and can be solved for x. Plug this into eq (2) and solve for y.

1) 2x+3y=7 and x-3y=2

Elimination method consists in the canceling of the unknown "x" or "y", by subtracting one eq. from the other. The first step is to look at both unknows to see which of them is easy to eliminate by subtracting.

In our case, it's obvious that the unknown y could be eliminated by adding the equation x-3y=2 to the eq. 2x+3y=7.

2x+3y+x-3y=7+2

3x=9

x=9/3

**x=3**

Now, you can replace the found unknown in what eq. you want.

For example,

x-3y=2, x=3

3-3y=2

-3y=-3+2

-3y=-1

**y=1/3**

**2) 4x-2y=7 and x-2y=1**

In this case, it's obvious that also the unknown y could be eliminated by subtracting the equation x-2y=1 from the eq. 4x-2y=7.

4x-2y -(x-2y) =7-1

4x-2y -x + 2y =6

3x=6

x=6/3

**x=2**

Again, you can replace the found unknown in what eq. you want.

For example,

x-2y=1, x=2

2-2y=1

-2y=1-2

-2y=-1

**y=1/2**

(1)2x+3y=7 and x-3y=2 (2) 4x-2y=7 and x-2y=1

Solutions:

(1)

2x+3y=7...........(1) and

x-3y =2............(ii)

Normally we use the technic of eliminating one variable and solve for the other single variable by reducing two equations to single equation as below.

Adding the two equations, we see that +3y in the 1st and -3y in the 2nd equation gets cancelled and the equation reduces to one equation in the variable x:

So, eq(1) + eq(2) gives:

3x +3y -3y = 7+2 =9 or

3x=9 or

x =9/3 =3 . So from 1st equation, 2*3+3y =7 oy 3y = 7-6=1 or y=1/3.

2)

4x-2y=7.....................(i)

and x-2y=1.................(ii)

Subracting the 2nd equation from the 1st, the second terms , -2y-(-2y) in the the equation makes y's eliminated:

4x-x -2y-(-2y) = 7-1 or

3x = 7-1 =6 or x= 6/3 =2 .

So from 2nd equation, x-2 = 1 putting x=2, weget:

2-2y = 1 or

-2y =1-2= -1 or

y=-1/-2 =1/2

i hope these helps: