Solve the following system of equations by the elimination m

Solve the following system of equations by the elimination method. Check your solution. {3x - 5y = 33 2x + 6y = -34 Select the correct choice below and fill in any answer boxes in your choice. There is one solution. The solution set is (Simplify your answer. Type an ordered pair.) Solve the following system of equations by the substitution method. Check your solutions. x - y = - 5 7x + 5y = - 47 All parts showing Select the correct choice below and fill in any answer boxes in your choice, if necessary. There is one solution The solution set is (Type an ordered pair Simplify your answer.) There are infinitely many solutions The solution set is the sat of all ordered pairs {(x, )}. where x is any real number (Typo on expression using x as the variable Simplify your answer) The solution set is the empty set. Solve the following system of equations by the substitution method Check the solutions {2x - 9y = 66 8x + 86 = y Solve the following system of equations by the elimination method Check your solution. {x - y = 10 - 5x + 5y = 2 Select the correct choice below and fill in any answer boxes in your choice, if necessary. There is one solution The solution set is (Simplify your answer Type an ordered pair.) There are infinitely many solutions. The solution set is the set of all ordered pairs{(x)}, where x is any real number (Type an expression using x as the variable.) The solution set i the empty set Select the correct choice below, and fill in any answer boxes in your necessary. There is one solution The solution set is (Type an ordered pair Simplify your answer. There are infinitely many solutions. The solution set is the se ordered pairs {(x.)} where x is any real number (Type an expression using x as the variable Simplify your ar The solution set is the empty set.

Solution

3x - 5y = 33
2x + 6y = -34 ---> x + 3y = -17

Multiply the second eqn by 3 :
3x + 9y = -51

So, we have :
3x - 5y = 33
3x + 9y = -51

Subtracting :
-14y = 84
y = -6

And x + 3y = -17
x + 3(-6) = -17
x - 18 = -17
x = -17 + 18
x = 1

So, solution was :
x = 1 , y = -6

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2x - 9y = 66
8x + 86 = y

Substituting :
2x - 9(8x + 86) = 66
2x - 72x - 774 = 66
-70x = 840
x = -12

And using 8x + 86 = y, we get :
y = 8(-12) + 86
y = -10

So, solution is :
x = -12 , y = -10

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x - y = -5
7x + 5y = -47

Mutliply the first one by 5 :
5x - 5y = -25
7x + 5y = -47

Adding :
12x = -72
x = -72/12
x = -6

And using x - y = -5, we have :
-6 - y = -5
-y = -5 + 6
-y = 1
y = -1

So solution is :
x = -6 , y = -1

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x - y = 10
-5x + 5y = 2

Multoiply the first equation by 5 :
5x - 5y = 50
-5x + 5y = 2

Adding these :
0 = 52, which is ABSURD

Now, when we tried eliminating, both variables got cancelled and we were left with statement 0 = 52, which is FALSE

So, conclusion is :

NO SOLUTION EXISTS