If anyone can help me solve these systems and show their work Iwill rank generou
ID: 3091240 • Letter: I
Question
If anyone can help me solve these systems and show their work Iwill rank generously.a) x + 2y - z = 3
2x - 2y + 3z = 4
2x + 10y - 7z = 8
b) 3x1 + x2 - 6x3 = 7
2x1 - x2 + x3 = 2
x1 - x2 + 2x3 = 3
Thank you!
Explanation / Answer
a) x + 2y - z = 3 2x - 2y + 3z = 4 2x + 10y - 7z = 8 First, solve [x + 2y - z = 3] for z: x + 2y - z = 3 => z = x + 2y - 3 Next, substitute for z in each of the three equations: x + 2y - z = 3 2x - 2y + 3z = 4 2x + 10y - 7z = 8 x + 2y + [x + 2y - 3] = 3 => 2x + 4y = 6 2x - 2y + 3[x + 2y - 3] = 4 => 2x - 2y + 3x + 6y - 9 = 4 => 5x + 4y = 13 2x + 10y - 7[x + 2y - 3] = 8 => 2x + 10y - 7x - 14y + 21 = 8 => -5x - 4y = -13 => 5x + 4y = 13 So the new system of equations is 2x + 4y = 6 5x + 4y = 13 5x + 4y = 13 Multiply each term of [2x + 4y = 6] by -2 and then add the threeequations: [-4x - 8y = -12] + [5x + 4y = 13] + [5x + 4y = 13] = [6x = 14] => x = 14/6 => x = 7/3 Now find y: 5x + 4y = 13 => y = (13 - 5(7/3))/4 => y = (39/3 - 35/3)/4 => y = (4/3)/4 => y = 4/12 => y = 1/3 Now find z: z = x + 2y - 3 => z = 7/3 + 2(1/3) - 3 => z = 7/3 + 2/3 - 9/3 => z = 0 Check: x + 2y - z = 3 2x - 2y + 3z = 4 2x + 10y - 7z = 8 (7/3) + 2(1/3) - (0) = 3 ... yes 2(7/3) - 2(1/3) + 3(0) = 4 ... yes 2(7/3) + 10(1/3) - 7(0) = 8 ... yes b) Maybe someone else will solve this one ... If you find this post helpful, please rate it.