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