How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36
Responses
infinite
infinite - not selected, this is the correct answer
one
one - no response given
none
none - incorrect
two
The correct answer is "infinite".
Give me step by step on why its infinite
To show that the system of equations has infinitely many solutions, we can start by manipulating one of the equations to match the other equation.
1. Rearrange the first equation −5x + y = −18 to solve for y:
y = 5x - 18
2. Now substitute this value of y into the second equation 10x - 2y = 36:
10x - 2(5x - 18) = 36
10x - 10x + 36 = 36
0 = 0
3. Since 0 = 0 is always true, it means that any value of x will satisfy this equation set when y = 5x - 18. This implies that for every value chosen for x, y will always be 5 times that value minus 18.
Therefore, the system of equations has infinitely many solutions because each of these infinite pairs of x and y values will satisfy both equations.