Solve the system of equations using elimination: 4, x, plus, 3, y, equals, minus, 114x+3y=−11 and minus, 9, x, minus, 9, y, equals, 18−9x−9y=18

Answer 1

First, let's rewrite the system of equations:

4x + 3y = -11
-9x - 9y = 18

Now, we can multiply the second equation by -1 to simplify the process of elimination:

4x + 3y = -11
9x + 9y = -18

Next, we can add the two equations together to eliminate the y variable:

(4x + 3y) + (9x + 9y) = (-11) + (-18)
13x + 12y = -29

Now, let's solve this new equation for x:

13x = -29 - 12y
x = (-29 - 12y)/13

Now, substitute this value of x into one of the original equations:

4(((-29 - 12y)/13)) + 3y = -11
((-116 - 48y)/13) + 3y = -11
-116 - 48y + 39y = -143
-116 - 9y = -143
-9y = -143 + 116
-9y = -27
y = -27/(-9)
y = 3

Now, substitute the value of y back into the equation for x:

x = (-29 - 12(3))/13
x = (-29 - 36)/13
x = -65/13
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3.