To find the solution of the system of equations, we can solve for each variable, x, y, and z.
First, let's solve for x. We can start by eliminating x from the second and third equations. Multiply the second equation by 5 and the third equation by -3:
10x - 30y + 10z = 15
-15x + 6y - 15z = -27
Now, add these two equations together:
10x - 30y + 10z - 15x + 6y - 15z = 15 + (-27)
-5x - 24y - 5z = -12
We can rewrite this equation as:
5x + 24y + 5z = 12
Now, let's eliminate x from the first and third equations. Multiply the first equation by 5 and the third equation by 3:
-15x - 20y - 15z = -35
15x - 6y + 15z = 27
Add these two equations together:
-15x - 20y - 15z + 15x - 6y + 15z = -35 + 27
-26y = -8
Divide both sides of the equation by -26:
y = -8 / -26
y = 4/13
Now that we have the value of y, we can substitute it back into the second equation to find z:
2x - 6(4/13) + 2z = 3
2x - 24/13 + 2z = 3
Let's rearrange this equation:
2x + 2z = 3 + 24/13
2x + 2z = 39/13 + 24/13
2x + 2z = 63/13
Now, let's eliminate x from the first and second equations. Multiply the first equation by 2:
-6x - 8y - 6z = -14
Add this equation to the second equation:
-6x - 8y - 6z + 2x - 6y + 2z = -14 + 3
-4x - 14y - 4z = -11
We can rewrite this equation as:
2x + 7y + 2z = 11/4
Now, let's set the expressions for 2x + 2z equal to 2x + 7y + 2z:
63/13 = 11/4
This equation is not true since the left side is in terms of x and z, and the right side is in terms of x and y. Therefore, there is no solution for this system of equations.
In conclusion, there is no solution to the system of equations.
What is the solution of the system of equations?-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9
(5,-2,7
1 answer