How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36 (1 point)
Responses
none
none
infinite
infinite
one
one
two
one
The system of equations −5x+y=−18 and 10x−2y=36 has one solution.
To determine the number of solutions for the system of equations, let's solve them using the method of substitution or elimination.
Given the system of equations:
−5x + y = −18 -- (Equation 1)
10x − 2y = 36 -- (Equation 2)
Let's solve the system using the method of substitution:
Solve Equation 1 for y:
y = 5x - 18 -- (Equation 3)
Substitute Equation 3 into Equation 2:
10x - 2(5x - 18) = 36
Simplify the equation:
10x - 10x + 36 = 36
36 = 36
The equation is true, but it does not provide any specific value for x or y since the variable x cancels out. This indicates that the two equations are equivalent, which means they represent the same line on the coordinate plane.
Therefore, the system of equations has infinite solutions.