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Mathematical problems in solving ternary linear equations
8.4 An example of solving ternary linear equations

1. In the equation 5x-2y+z = 3, if x =- 1 and y =-2, then z = _ _ _ _ _

2. Given the monomials -8a3x+y-zb 12cx+y+z and 2a4b2x-y+3zc6, then x = _ _ _ _, y = _ _ _, and z = _ _ _ _.

3. Solve the equations X+Y-Z = 1 1, Y+Z-X = 5, Z+X-Y = 1, then X = _ _ _ _, Y = _ _ _ _, and Z = _ _ _ _.

4. Given the algebraic expression AX2+BX+C, when x =- 1, its value is 4; When x = 1, its value is 8; When x = 2, its value is 25; Then when x = 3, its value is _ _ _ _ _.

5. Given that x-3y+2z = 0 3x-3y-4z = 0, then x: y: z = _ _ _ _ _.

6. Solve the equations x+y-z =11y+z-x = 5z+x-y =1. In order to make the operation simple, the elimination method () should be selected.

A, first eliminate x B, first eliminate y C, first eliminate z D, all the above statements are wrong.

7. The solution of the equation system x+y =- 1x+z = 0y+z = 1 is ().

a . x =- 1y = 1z = 0b x = 1y = 0z =- 1c x = 0y = 1z =- 1

D x=- 1 y=0 z= 1

8. If x+2y+3z = 10 and 4x+3y+2z = 15, the value of x+y+z is ().

a、2 B、3 C、4 D、5

9. If the solution x of the equation set 4x+3y =1ax+(a-1) y = 3 is equal to y, then the value of a is equal to ().

a、4 B、 10 C、 1 1 D、 12

10. Given ∣ x-8y ∣+2 (4y-1) 2+3 ∣ 8z-3x ∣ = 0, find the value of x+y+z y+z.

1 1. Solve the equation x+y-z = 6x-3y+2z =13x+2y-z = 4.

12. The age of a couple is 6 times that of their children now, 10 times that of their children two years ago, and 3 times that of their children six years later. How many children do the couple have?

13.3x-z=0 3y=2z x+y+z=6

14 . 2x+y-z = 2x+2y-z = 5x-y+2z =-7

15.x+y=3 y+z=5 x+z=6