Eliminate one of the variables using the second equation.
(-1, 12,2)
Practice makes perfect
We want to solve the following system of equations.
5x-4y-6z=-19 & (I) -2 x+2y+z=5 & (II) 3x-6y-5z=-16 & (III)
Note that the coefficient of y in the second equation allows us to eliminate it from the remaining equations. It divides and is opposite to the coefficients of y in the first and the third equation.
5x- 4y-6z=-19 -2 x + 2y+z=5 3x- 6y-5z=-16
Therefore, we will use the Elimination Method. To eliminate y from the first equation we should add the second equation multiplied by 2.
5x - 4y - 6z + 2( -2 x + 2y + z )=-19 + 2( 5) -2 x+2y+z=5 3x-6y-5z=-16
Let's simplify the first equation.
Similarly, we can eliminate y from the third equation by adding the second equation multiplied by 3.
x - 4z=-9 -2 x+2y+z=5 3x - 6y - 5z + 3( -2 x + 2y + z )=-16 + 3( 5)
Now, let's simplify the third equation.
The first and the third equation consists only of 2 variables. Note that we can isolate x in the first equation by adding 4z to both sides.
x- 4z=-9 -2 x+2y+z=5 -3 x-2z=-1 ⇕
x= 4z-9 -2 x+2y+z=5 -3 x-2z=-1
Once we have isolated x, we can substitute its equivalent expression into the third equation and solve for z.
