How many solutions are there for the linear system x – y = –5 and x + y = 1?
Eq1: x - y = -5
Eq2: x + y = 1
Add the Eqs:
2x = -4
X = -2.
In Eq2, substitute -2 for X:
-2 + y = 1
Y = 3.
Solution = (x,y) = (-2,3).
The lines intersect @ only 1 point.Therefore, we have only one solution.
To find the number of solutions for a linear system, such as the one given here, we can use the concept of elimination or substitution.
Let's start with elimination. We have the following system of equations:
x - y = -5 ---(1)
x + y = 1 ---(2)
To eliminate one variable, we can sum the two equations. Adding equation (1) and equation (2), we get:
(x - y) + (x + y) = -5 + 1
Simplifying the equation, we have:
2x = -4
Dividing both sides of the equation by 2, we get:
x = -2
Now, we can substitute this value of x back into either equation (1) or (2). Let's substitute it into equation (2):
x + y = 1
-2 + y = 1
To find y, we can isolate y by adding 2 to both sides of the equation:
y = 3
So, we have found the values of x and y, which are x = -2 and y = 3.
Since we have found specific values for both x and y, the linear system has a unique solution. In other words, there is only one solution for this linear system.
Therefore, the number of solutions for the linear system x - y = -5 and x + y = 1 is one.