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

Expert Answers
justaguide | Certified Educator

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.

chaobas | Student

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

vaaruni | Student

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

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