Determine the solution to the system of equations below.%0D%0A%0D%0A-5x – 7y = 11 %0D%0A%0D%0Ax – 2y = -9%0D%0AResponses%0D%0A%0D%0A%0D%0AA%09Infinitely many solutionsInfinitely many solutions%0D%0A%0D%0A%0D%0AB%09x = -5, y = 2x = -5, y = 2%0D%0A%0D%0A%0D%0AC%09No solutionNo solution%0D%0A%0D%0A%0D%0AD%09x = -5, y = -7
The correct answer is D) x = -5, y = -7.
To solve this system of equations, we can use the substitution method.
From the second equation, we can express x in terms of y:
x = 2y - 9
Now, we can substitute this expression for x into the first equation:
-5(2y - 9) - 7y = 11
-10y + 45 - 7y = 11
-17y + 45 = 11
-17y = -34
y = -34 / -17
y = 2
Now that we have found the value of y, we can substitute it back into the second equation to find x:
x = 2(2) - 9
x = 4 - 9
x = -5
Therefore, the solution to the system of equations is x = -5, y = -7.