How do you solve simultaneous equations using the substitution method ?

x=y 6x-2y=10 x=-y 3x-6y=36

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So these are two separate simultaneous equations, right? And x actually equals y in the first one?

If so, in the first one, just substitute y for x. Then you will have 6y - 2y = 10. That becomes 4y = 10 and that becomes y = 2.5.

The other one is a little more complicated since x = -y, but it's the same process. You substitute -y for x. Then you will have

-3y - 6y = 36

That gets you

-9y = 36

And y = -4

Since x = -y, x = -(-4). Two negatives make a positive and x = 4

I am assuming that we are talking about 2 different systems since x=y in the first and x=-y in the second.

For the first system where x = y, simply substitute x for y. Then 6x - 2y becomes 6x -2x. So 6x -2x = 4x =10. Divide both sides by 4 and you have x = 2.5 => y = 2.5.

For the second system:

Since x = -y, then replace x with -y. Then 3x - 6y becomes 3(-y) - 6y. Now, we have -3y - 6y = -3y + -6y = -9y =36. Divide both sides by -9 and we have y= - 4 => -y = 4 => x = 4.

If you need to solve each with x=y and x=-y, then you would follow the same steps for the other equation. In other words, use x = -y for substituting in 6x - 2y. Then you would have 6(-y) - 2y = -6y - 2y = -8y = 10. Divide both sides by -8 and get y = -1.25. Since x= -y, the x = 1.25.

Simultaneous equations are solved by substituting one variable for the other and setting the equation equal to 0, or if it has a constant. This is simply done by exchanging one for the other, for example, x=y, 6x-2y=10. You have to substitute y for x and the equation becomes:

6y-2y=10

4y=10

y=2.5

The other equations for y, substituting x for y is the same process.

3x-6y=36

-3y-6y=36

-9y=36

y=-4.

It is a very easy and straightforward process for you to solve similar equations using the same process.

There are two pairs pair of equations, each pair having two variables x and y.

First pair:

x=y.....................(i) and

6x-2y=10.............(ii)

are simultaneous linear equations in two variables x and y.

Since x=y , substitute y = x in (ii) and we get: 6x-2x = 10. Or 4x = 10 . Therefore, x = 10/4 = 2.5. Since y = x, y = 2.5

Second Pair:

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

3x-6y=36 ...........(2).

Though it is easy to substitute x= -y, we go different. From the second equation (dividing both sides by 3) we get x-2y = 12 . Or x = 12+2y. Substituting this x in terms of y in (1), we get:

12+2y = -y Or Subtracting 2y from both sides, we get:

12 = -3y Or y = 12/-3 = -4. So x =-y = -(-4) = 4.

The substitution method involves replacing the variable in one equation with another variable. For example, in both cases we are told what x equals in terms of y. Replace every instance of x in the other equation with this y value. Then you will have only one equation in terms of y which you can solve for easily. Then plug this back into the other equation to solve for x.

Substitution Method is used to solve simultaneous equations, as given above. To solve simultaneous equations the following steps should be taken:

Label the equations as i and ii,

x=y ------(i)

6x-2y=10 ------(ii)

The next step is to isolate one variable from any equation, which has been done already as x=y.

After this step input the value of x in eq(ii) and solve to get the value of y:

6x-2y=10 ------(ii)

6y-2y=10

4y=10

4y/4=10/4 divide both sides by 4

**y=2.5**

After this we would have to input this value in equation ii, but since it has already been determined that x=y we can say that x=2.5 as well.

**x=2.5**

**y=2.5**

To further check the answers input both values in eq(ii)

6x-2y=10

6(2.5)-2(2.5)=10

15-5=10

10=10

LHS=RHS proved.

The same steps are to be followed in this one:

x=-y -------(i)

3x-6y=36 -------(ii)

Input the value of x in eq(ii)

3x-6y=36

3(-y)-6y=36

-3y-6y=36

-9y=36

-9y/-9=36/-9 divide both sides by -9

**y=-4**

Now since both value are equal only their signs are different i.e. x=-y therefore **x=4**.

Input both value in eq(ii) to check if they are correct:

3x-6y=36 -------(ii)

3(4)-6(-4)=36

12+24=36

36=36

LHS=RHS proved.

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