Question

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

y= -x + 5 y= x - 3

Answer 1

The following equation has:

Unique solution (one solution i.e. (4,1) )

Explanation:

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:

`-x+5=x-3`

On adding x on both the sides of the equation we have:

`5=x+x-3\\\\5=2x-3`

on adding 3 on both the sides of the equation we have:

`2x=5+3\\\\2x=8\\\\x=(8)/(2)\\\\x=4`

Now, on putting the value of x into equation (2) we have:

`y=4-3\\\\y=1`

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.

Answer 2

The system has one solution: (4,1)

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.