To find the number of solutions to the system of equations, we can solve the system and determine if the equations intersect at a single point (one solution), if the equations are parallel and do not intersect (no solution), or if the equations coincide and intersect at infinitely many points (infinite solutions).
First, let's solve the system of equations by substitution.
From the first equation, we know that y = x + 3. We can substitute this expression for y in the second equation to solve for x:
3x + (x + 3) = -1
4x + 3 = -1
4x = -4
x = -1
Substituting this value of x back into the first equation, we can solve for y:
y = -1 + 3
y = 2
Therefore, the solution to the system of equations is x = -1 and y = 2.
Since we have found a unique solution, there is only one solution to the system of equations.
Identify the number of solutions to the system of equation:
y=x+3
3x+y=-1
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