To find the number of solutions to the system of equations, we can solve the equations and determine if they intersect at a single point, are parallel and non-intersecting, or are the same line.
First, let's solve the system of equations:
y = x + 3
3x + y = -1
Rearranging the second equation, we get:
y = -3x - 1
Now we can equate the two expressions for y:
x + 3 = -3x - 1
Adding 3x to both sides:
4x + 3 = -1
Subtracting 3 from both sides:
4x = -4
Dividing both sides by 4:
x = -1
Substituting this value back into the first equation:
y = -1 + 3
y = 2
Therefore, we have found a single solution for the system of equations: x = -1 and y = 2.
Since the equations intersect at a single point, the system has exactly one solution.
1. Identify the number of solutions to the system of equation:
y=x+3
3x+y=-1
1 answer