# Show that <w, x, y, z>= <2,0,-1,3>is a particular solution for the system w+ 3x + 2y -3z = -9 -3w -6x + 3y -4z = -21 4w -5x -3y + 3z = 20

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Expert Answers

sciencesolve | Certified Educator

You need to test if `<w, x, y, z> = <2,0,-1,3>` is a particular solution to the system, replacing 2 for w, 0 for x, -1 for y, 3 for z in each equation of the system and checking if each equation holds for these values, such that:

`2 + 3*0 + 2*(-1) - 3*3 = -9 => 2 - 2 - 9 = -9 => -9 = -9` valid

`-3*2 - 6*0 + 3*(-1) - 4*3 = -21 => -6 - 3 - 12 = -21 => -21 = -21` valid

`4*2 - 5*0 - 3*(-1) + 3*3 = 20 => 8 + 3 + 9 = 20 => 20 = 20`

**Hence, testing the values `<w, x, y, z> = <2,0,-1,3>` in each equation of the system yields that they hold for these values, hence `<w, x, y, z> = <2,0,-1,3>` represents a particular solution to the system.**