solve the system of equations

Question

-3x - 4y - 3z = -7
2x - 6y + 2z = 3
5x - 2y + 5z = 9

A. (5, -2, 7)
B. (-5, 2, 7)
C. (5, 2, -7)

Answer 1

To solve this system of equations, we can use the method of elimination or substitution.

Let's use the method of elimination. We will eliminate the variable z.

Multiply the first equation by 2:
-6x - 8y - 6z = -14

Multiply the second equation by 3:
6x - 18y + 6z = 9

Add these two equations together:
0x - 26y + 0z = -5

Simplify:
-26y = -5

Solve for y:
y = -5 / -26
y = 5/26

Substitute y = 5/26 into the first equation:
-3x - 4(5/26) - 3z = -7
-3x - 20/26 - 3z = -7
-3x - 10/13 - 3z = -7
-3x - 3z = -7 + 10/13
-3x - 3z = -91/13

Multiply the third equation by 4:
20x - 8y + 20z = 36

Add this equation to the fourth equation:
-3x - 3z + 20x - 8y + 20z = -91/13 + 36
17x + 17z - 8y = -91/13 + 468/13
17x + 17z - 8y = 377/13

Substitute y = 5/26 into this equation:
17x + 17z - 8(5/26) = 377/13
17x + 17z - 40/26 = 377/13
17x + 17z - 20/13 = 377/13
17x + 17z = 397/13

Now we have a system of two equations:
-3x - 3z = -91/13
17x + 17z = 397/13

Multiply the second equation by -1/3 and add it to the first equation:
-3x - 3z -1/3(17x + 17z) = -91/13 -1/3(397/13)
-3x - 3z -17/39x - 17/39z = -91/13 - 397/39
-3x - 17/39x - 3z - 17/39z = -91/13 - 397/39
(-3 - 17/39)x + (-3 - 17/39)z = (-13*91 - 397)/13*3

Solve for x:
(-194/39)x + (-194/39)z = -5140/39
(-194x -194z) / 39 = -5140/39
-194x - 194z = -5140

Divide throughout by -194:
x + z = 26 and simplify, we get
x + z = 40/3

Using that x + z = 26, we know that z = 40/3 - 26= 40/3 - 78/3 = -38/3

Then, solving for x using x + z = 26:
x + (-38/3)= 26
x = 26 + 38/3 = 78/3 + 38/3 = 116/3 =38 and 2/3

So, the solution to the system of equations is (38 and 2/3, 5/26, and -38/3), which is approximately (11.67, 0.19, -12.67).

Thus, the answer is not listed in the given choices.