Question

Solve the given system of equations. X+ y + 6z = -25 X+ y + 4z = - 17 X-9y + 8z = 7 Select the correct choice below and fill in any answer boxes within your choice. )}. (Simplify your answers.) O A. There is one solution. The solution set is {(1 OB. There are infinitely many solutions. O C. There is no solution. Click to select and enter your answer(s).

Answer 1

The solutions are: x = 3, y= -4, z= -4 Explanation: Step 1: Multiply first equation by -1 and add the result to the second equation. The result is: 2 + y + 6 z - 2 z + 82 = – 25 = 8 = 7 X - 9 y Step 2: Multiply first equation by –1 and add the result to the third equation. The result is: x + y + 6 z - 2 2 + 2 2 = = = – 25 8 32 - 10y Step 3: Swap Row 2 and Row 3.After this step we have: 2 + y – 10 y + 6 z + 2z - 2z = – 25 = 32 = 8 Step 4: solve for z. z= 8 2= -4 Step 5: solve for y. -10y + 2z = 32 -10y +2.(-4) = 32 y= -4 Step 6: solve for x by substituting y = -4 and z = -4 into the first equation.

xy=9 & 9x^2+y^2=90? use substitution: x=9/y plug into 2-9(9/y)^2+y^2=90 729/y^2+y^2=90 =729/y^2+y^4/y^2=90 729+y^4=90y^2 y^4-90y^2+729=0 (y^2-9)(y^2-81)=0 y^2=9, 81 y=+3, +9, -3, -9 so when y=3, x=3 when y=9, x=1 when y=-3, x=-3 and when y=-9, x=-1