5x+3y-5z=54 ...(1)
2x-3y+2z=-7 ...(2)
4x-2y+4z=-2 ...(3)
Let's add equation (1) and (2) to eliminate y.
So, (5x+2x)+(3y-3y)+(-5z+2z)=54-7
7x-3z=47 ...(4)
Now we need to make the equal coefficient of y's of equation (2) and (3) to eliminate y by using these two equations.
So, multiply equation (2) by 2 and (3) by -3. Therefore,
2*(2x-3y+2z=-7) 4x-6y+4z=-14
-3*(4x-2y+4z=-2) -12x+6y-12z=6
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-8x-8z=-8 (By adding two equations).
x+z=1 (Divided each sides by -8). ...(5)
3x+3z=3 (Multiply each sides by 3)
Now add this equation with equation (4)
3x+3z=3
7x-3z=47
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10x=50
So, x=5 (Divided each sides by 10).
Now plug in x=5 in equation (5). So,
5+z=1
z=1-5
z=-4
Now plug in the values of x and z in equation (1) to get the value of y. So,
5(5)+3y-5(-4)=54
25+3y+20=54
3y+45=54
3y=54-45
3y=9
y=3.
So, the solution set is x=5, y=3 and z=-4.
