Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
minus, 5, x, plus, 3, y, equals, minus, 9
−5x+3y=
−9
minus, 20, x, plus, 11, y, equals, minus, 48
−20x+11y=
−48
Answer
Multiple Choice Answers
One SolutionOne Solution
Infinitely Many SolutionsInfinitely Many Solutions
No SolutionsNo Solutions
To determine the number of solutions, we can solve the system of equations using a method such as substitution or elimination.
Let's solve the system using elimination:
Multiply the first equation by 11 and the second equation by 3 to make the coefficients of y equal:
-55x + 33y = -99
-60x + 33y = -144
Now subtract the second equation from the first equation to eliminate y:
(-55x + 33y) - (-60x + 33y) = -99 - (-144)
-55x + 33y + 60x - 33y = -99 + 144
5x = 45
x = 9
Substitute the value of x into the first equation to solve for y:
-5(9) + 3y = -9
-45 + 3y = -9
3y = 36
y = 12
So the solution to the system of equations is x = 9 and y = 12. Therefore, the system has exactly one solution.