Just make up 9 numbers, positive or negative
at random, and use them as coefficients for
x, y and z.
I made up these 9 numbers, completely at random
2,-5,3,-3,4,-2,1,5,-4
and put them as coefficients of x,y, and z, like this:
followed by an equal sign
2x-5y+3z =
-3x+4y-2z =
x+5y-4z =
Then I substituted x=-2,y=3,and z=4 in each one, like this:
2(-2)-5(3)+3(4) = -4-15+12 = -7
-3(-2)+4(3)-2(4) = 6+12-8 = 10
(-2)+5(3)-4(4) = -2+15-16 = -3
Then I put those results after the equal signs,
and got this system of 3 equations and 3 unknowns:
2x-5y+3z = -7
-3x+4y-2z = 10
x+5y-4z = -3
That system has the solution set (x,y,z) = (-2,3,4)
You can make up as many as you like. This is
how teachers and people who write math books
make up problems for students to solve.
Edwin
