## Solving by substitution method, Page 2

Solving system of equation by substitution method, involves solving any one of the given equation for either 'x' or 'y' and plugging that in the other equation and solve that equation for another variable.

Example 1:

2x+y=-1

3x+5y=2

Solution:

In the given two equations, the first equation has only 'y' term. So let us solve for y in the first equation.

2x+y=-1 ----(1)
3x+5y=2 ----(2)

Now we need to solve the value for y in terms of x from the first equation.For that we have to subtract by 2x on both sides.

2x + y = -1
-2x      -2x
----------------
y = -1-2x
----------------
Now we have to plug y = -1-2x in the second equation.
3x+5(-1-2x)=2
3x - 5 -10x = 2
7x - 5 = 2
7x - 5 + 5 = 2 + 5
7x = 7
dividing by 7 on both sides
7x/7 = 7/7
x = 1
Now we have to plug x = 1 in y = -1 -2x
So that we will get y = -1 -2(1)
y = -1-2
y = -3
Therefore the solution is (1,-3).

Example 2:

Solve the following equations by using substitution method:

y = 10-2x

x +y/2 = 5

Solution:

Here we have y value in the first equation. So let us plug in the value in the second equation, x+ y/2 = 5.

x + (10-2x)/2 = 5 x + (10/2) + (-2x/2) = 5

x + 5 - x = 5

5 = 5

which is a unhelpful result, which implies that both the equations represents the same line. So the system of equations is dependent equation.

If we solve by graphical method, (Page 1)we will get the following graph which implies that both the equations represent the same line.

So the system of equations is dependent system Example 3:

Solve the following system of linear equations by substitution method:

2x+4y = -8

3x-2y =12

Solution: ### Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

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