# x-2y=-4 2x-y=1

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This is an example of simultaneous equations.

These may be solved by eliminating a variable as follows:

a) x-2y=-4 multiply the equation by 1 ==> x-2y=-4

b) 2x-y=1 multiply the equation by 2 ==> 4x-2y=2

Now subtract the result of a) from b) :- 4x-2y=2 or 4x-2y=2

- ( x-2y=-4) -x+2y=4

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The result is 3x = 6 or x =2, now substitute this value in any equation above containing y for a) x - 2y = -4, becomes upon substituting x =2

2 -2y = -4 or (subtracting 2 from both sides) -2y = -6 and (dividing by -2)

y=3

`x-2y=-4` Let this be EQ1.

`2x-y=1` Let this be EQ2.

To solve this system of equations, we may use substitution method. To apply it, let's isolate the x in EQ1.

`x-2y=-4`

`x-2y+2y=-4+2y`

`x=2y-4`

Then, plug-in that to EQ2.

`2x-y=1`

`2(2y-4)-y=1`

And, solve for y.

`4y-8-y=1`

`3y-8=1`

`3y-8+8=1+8`

`3y=9`

`(3y)/3=9/3`

`y=3`

Now that the value of y is known, let's solve for x. To do so, plug-in that to

`x=2y-4`

`x=2(3)-4`

`x=6-4`

`x=2`

**Therefore, the solution to the given system of equations is (2,3).**

We can solve these equations with the help of substitution method.

x - 2y = -4 ------ eq(i)

2x - y = 1 ------ eq(ii)

Consider eq(i), in it isolate x

x - 2y = -4

x = - 4 + 2y

Input this value in eq(ii)

2x - y = 1

2(- 4 + 2y) - y = 1

-8 + 4y - y = 1

-8 + 3y = 1

-8 + 3y + 8 = 1 + 8 Add 8 to both sides

3y = 9

3y/3 = 9/3 Divide both sides by 3

**y = 3**

Input The value of y in eq(i)

x - 2y = -4

x - 2(3) = -4

x - 6 = -4

x - 6 + 6 = -4 + 6 Add 6 to both sides

**x = 2**

Therefore

**x = 2**

**y = 3 Answer.**

Now to verify, input the value of x and y in any equation,

x - 2y = -4 ------ eq(i)

2 - 2(3) = -4

-4 = -4

LHS=RHS Proved.

x-2y=-4

2x-y=1

x-2y=-4

+2y

x=2y-4

2(2y-4)-y=1

3y-8=1

y=3

x-2(3)=-4

x=2

To start off with this question we will have to label both equations

x-2y=-4 This will be equation A

2x-y=1 This will be equation B

The first step you want to do is figure out which variable you want to find first I will choose to solve for y first. Now I am going to take equation A and multiply the entire eqution by -2. Doing this will cancel out the x's as you add the entire equation

`A:-2(x-2y)=(-4)-2`

`A:-2x+4y=8`

`B:2x-y=1`

This will give you the equation 3y=9 now divide 3 on both sides and you will get...

y=3

Now take either of the equations (it doesn't matter they will give you the same answer) and substitute y with 3 in order to find the value of x. I will be using equation B.

`B: 2x-3=1`

`2x=4`

`2/2x=4/2`

`x=2`

` ` There you go the answers for both variables!

x=2 y=3

X=2 :D