# What is the solution of x + y = 18 and 2x + 2y = 21

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The equations x + y = 18 and 2x + 2y = 21 have to be solved.

2x + 2y = 21 can be rewritten as x + y = 10.5

The lines represented by x + y = 18 and x + y = 10.5 are parallel to each other and do not intersect at any point.

** The given system of equations is indeterminate and there is no solution.**

The given equation are x + y = 18 and 2x + 2y = 21

let make this equation in y=mx+c form

x + y = 18

y=-x+18 so slope is -1 (m)

and

2x + 2y = 21

2y=-2x+21[dividing both side by 2]

y=-x+(21/2) so m=-1

now we can see that these two equation have same slope.

**"If the slope of two line(equation) are equal then they are parallel, that is there is no solution for the equation"**

So there is no solution for the two equation

Both the equations represents the equation of a straight line .

Let first equation x + y = 18 represents the line AB and

the second equation 2x + 2y = 21 represents the line CD

We can express this equation x + y =18 as

y = -x +18 [in the form y=mx+c]

Here we get the slope of the line AB (m1) = -1 -----(1)

Let us take the second equqtion 2x + 2y = 21

Now we express this equation also in the form of y = mx + c

We get 2y = -2x + 21

Or, y = (-2x)/2 +( 21) /2

Or, y = -x + 21/2

The slope of the line CD (m2) = -1 ------(2)

From (1) and (2) we got m1 = m2

Since the slope of the two lines are equal which indicates/proves that the two lines are **parallel** to each other and do not intersect eachother at any point

**Hence the given system of equations have no solution**