Solce the system using the linear combination method.
5x-3y+2z=3
2x+4y-z=7
x-11y+4y=3
I already knw that there is no soulution for it but its not coming up like that on my work.
first equation + twice the second yields
9x + 5y = 17
double the first equation - last equation yields
9x + 5y = 3
thus no solution.
To solve the system of equations using the linear combination method, we need to eliminate one variable at a time by adding or subtracting equations. In this case, it seems that you made a mistake in the third equation. The equation should be:
x - 11y + 4z = 3
Let's proceed with solving the system using the linear combination method:
Given equations:
1) 5x - 3y + 2z = 3
2) 2x + 4y - z = 7
3) x - 11y + 4z = 3
We will start by eliminating the x variable. To do this, we can multiply equation 2 by 5 and equation 3 by -2, then add equation 1, equation 2, and equation 3:
5*(2x + 4y - z) + (-2)*(x - 11y + 4z) + (5x - 3y + 2z) = 5*7 - 2*3 + 3
This simplifies to:
10x + 20y - 5z - 2x + 22y - 8z + 5x - 3y + 2z = 35 - 6 + 3
Combining like terms:
10x - 2x + 5x + 20y + 22y - 3y - 5z - 8z + 2z = 32
Simplifying further:
13x + 39y - 11z = 32
Now, let's eliminate the y variable. To do this, we can multiply equation 1 by 13 and equation 3 by 3, then subtract equation 1 from equation 3:
3*(5x - 3y + 2z) - 13*(x - 11y + 4z) = 3*3 - 13*7
This simplifies to:
15x - 9y + 6z - 13x + 143y - 52z = 9 - 91
Combining like terms:
15x - 13x - 9y + 143y + 6z - 52z = -82
Simplifying further:
2x + 134y - 46z = -82
Now, we have the following two equations:
1) 13x + 39y - 11z = 32
2) 2x + 134y - 46z = -82
At this point, we can see that the system of equations has no unique solution. This might be due to inconsistent or dependent equations.