5. 1) C. 3/2·x + y = 2 ↔ y = -3/2·x + 2
6. 2) A. y = -2/3·x + 2 ↔ 2·x + 3·y = 6
7. 3) D. y = 3/2·x + 2 ↔ y = 3/2·x + 2
8. 4) E. y = 2·x + 2 ↔ -6·x + 3·y = 6
9. 5) B. 3·x + y = 6 ↔ y = -3·x + 6
10. 6) y = 5/4·x - 10, and y = 5/4·x - 11
11. 7) y = -8·x + 15 and y = -8·x + 16
12. 8) 4·x + y = 7 and 4·x + y = 6
13. 9) No
14. 10) Yes
Step-by-step explanation:
Two equations will have an infinitely many solutions when that represent the same equation
5. 1) C. 3/2·x + y = 2 is the same equation as y = -3/2·x + 2
6. 2) A. y = -2/3·x + 2 is the same equation as 2·x + 3·y = 6 (divide by 3 and make y the subject of the equation)
2·x/3 + 3·y/3 = 6/3 = 2
y = -2/3·x + 2
7. 3) D. y = 3/2·x + 2 is the same equation as y = 3/2·x + 2
8. 4) E. y = 2·x + 2 is the same equation as -6·x + 3·y = 6
-6·x/3 + 3·y/3 = 6/3 = 2
y = 6·x/3 + 2 = 2·x + 2
9. 5) B. 3·x + y = 6 is the same equation as y = -3·x + 6
3·x + y = 6
- 3·x + 3·x + y = -3·x + 6
y = -3·x + 6
Two straight line equations of the form, y = m·x + c, will have no solutions if they represent parallel lines and therefore, have equal slopes, m and different "y" intercepts, c
10. 6) For y = 5/4·x - 10, we have the slope, m = 5/4 and the "y" intercept c = -10
Therefore, the equation that will make a system with "no solution" has the same value for "m" and a different value for "c" such as y = 5/4·x - 11
11. 7) For y = -8·x + 15, similarly we have a system with "no solution" as follows;
y = -8·x + 15 and y = -8·x + 16
12. 8) For 4·x + y = 7, a system with "no solution" can be written as follows;
4·x + y = 7
∴ y = - 4·x + 7 which gives;
y = - 4·x + 7 and y = - 4·x + 6
From y = - 4·x + 6, we have;
4·x + y = 6
The system with "no solution" can therefore also be written as follows;
4·x + y = 7 and 4·x + y = 6
13. 9) No the sum of the two numbers and the result forms a function with the sum of the two numbers being the inputs of the function and their value, 8 being the output of the function and therefore, the input of a function can not have multiple outputs which are 8 and 10 which makes it not possible
14. 10) Yes, by the definition of a function, it is possible for two different inputs to a function to have the same output, therefore, given that the operation performed on the two inputs are different, the two inputs can be considered as different an can have he same output
For example, we have 8 + 0 = 8 and 8 - 0 = 8.
