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)
D. No solution

Answer 1

To solve this system of equations, we can use the method of elimination. We can eliminate the variable x by multiplying the first equation by 2 and the second equation by -3, and then adding the two resulting equations together:

2(-3x - 4y - 3z) = 2(-7)
-3(2x - 6y + 2z) = -3(3)

Simplifying these equations, we get:

-6x - 8y - 6z = -14
-6x + 18y - 6z = -9

Adding these two equations together, we obtain:

-6x - 8y - 6z + (-6x + 18y - 6z) = -14 + (-9)
-12x + 10y = -23

Now, we can solve this equation for y:

10y = 12x - 23
y = (12x - 23)/10

Next, we substitute this expression for y into the first equation:

-3x - 4((12x - 23)/10) - 3z = -7

Simplifying this equation, we have:

-3x - (48x - 92)/10 - 3z = -7
-30x - 48x + 92 - 30z = -70
-78x - 30z = -162

Finally, we substitute the expression for y into the third equation:

5x - 2((12x - 23)/10) + 5z = 9

Simplifying this equation, we get:

5x - (24x - 46)/10 + 5z = 9
50x - 24x + 46 + 50z = 90
26x + 50z = 44

So, the system of equations has no solution. The correct answer is D) No solution.