Answer:
The system has one solution: (4,1)
Step-by-step explanation:
We have the equations:
1) Y = -X + 5
2) Y = X - 3
Replace the "value" of Y of the 2nd eq into the 1st eq:
(X - 3) = -X + 5
Now let's leave X alone in one side of the iquality:
X + X = 5 + 3
2X = 8
X = 8/2
X = 4
Now, having the value of X, replace it into any of the aquations, let's use the 2nd:
Y = X - 3
Y = 4 -3
Y = 1
The ONE solution of this equations system is (4,1), which is the point in the xy plane where the two lines intersect.
The following equation has:
Unique solution (one solution i.e. (4,1) )
The system of equation is given by:
y= -x + 5-----------(1)
and y= x - 3------------(2)
Now, on substituting the value of y from equation (1) into equation (2) we have:
[tex]-x+5=x-3[/tex]
On adding x on both the sides of the equation we have:
[tex]5=x+x-3\\\\5=2x-3[/tex]
on adding 3 on both the sides of the equation we have:
[tex]2x=5+3\\\\2x=8\\\\x=\dfrac{8}{2}\\\\x=4[/tex]
Now, on putting the value of x into equation (2) we have:
[tex]y=4-3\\\\y=1[/tex]
Hence, the solution is unique (one solution )
Also, the point of intersection of the graph of two equations is solution to the system of equations.
