What is the solution to the linear system –4x + 2y = –56 and –3x – 6y = 33?Question 3 options:
(–9, 10)
(–9, –10)
(9, 10)
(9, –10)
To find the solution to the linear system –4x + 2y = –56 and –3x – 6y = 33, we can use the method of substitution or the method of elimination.
Let's solve the system using the method of elimination:
Step 1: Multiply the second equation by 2 to make the coefficients of y in both equations the same:
-4x + 2y = -56
-6x - 12y = 66
Step 2: Add the two equations together to eliminate the y variable:
(-4x + 2y) + (-6x - 12y) = (-56) + (66)
-10x - 10y = 10
Step 3: Divide through by -10 to solve for x:
-10x/-10 - 10y/-10 = 10/-10
x + y = -1
Step 4: Substitute the value of x into one of the original equations to solve for y:
-4x + 2y = -56
-4(-1) + 2y = -56
4 + 2y = -56
2y = -60
y = -30
Step 5: Substitute the values of x and y into the other original equation to check the solution:
-3x - 6y = 33
-3(-1) - 6(-30) = 33
3 + 180 = 33
183 = 33 (which is false)
Since the last equation does not hold true, the given system of equations has no solution. Therefore, none of the options (–9, 10), (–9, –10), (9, 10), or (9, –10) is correct.
-12 x + 6 y = -168
- 3 x - 6 y = 33
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-15 x = -135
x = +9
-3*9 - 6 y = 33
-27 -33 = 6y
y = -10
so (9,-10)