Solve the system by elimination, or by any convenient method.
A) And
B) And
C) And
D) And
E) And

Question

Solve the system by elimination, or by any convenient method. ​  ​
A) And 
B) And 
C) And 
D) And 
E) And

Quizplus · Accepted Answer

There are multiple methods to solve systems of equations, but one common method is elimination. To use elimination, we want to manipulate the equations so that we can add them together and eliminate one of the variables. From there, we can solve for the remaining variable and substitute the value back into one of the original equations to find the value of the eliminated variable.

For this system, we can eliminate y by adding the two equations together. We get:

2x + 3y = 11
3x - 4y = -1
__________
5x - y = 10

Now we have one equation with only the variable x. We can solve for x by isolating it:

5x - y = 10
5x = y + 10
x = (y + 10)/5

Now we can substitute this expression for x into one of the original equations to solve for y:

11eb0d3b_9798_b16b_9790_61c07c136063_TB1243_11
x - 2y = 3

11eb0d3b_9798_b16c_9790_47dba4652ba0_TB1243_11
(y + 10)/5 - 2y = 3

Multiplying everything by 5 to eliminate the fraction:

y + 10 - 10y = 15
-9y = 5
y = -5/9

Now we can substitute back into the expression for x:

x = (y + 10)/5 = ( -5/9 + 10)/5 = 51/45

Therefore, the solution to the system is (x, y) = (51/45, -5/9).

Solve the System by Elimination, or by Any Convenient Method