the first statement: Systems A and C have the same solution the fourth statement: System C simplifies to 2x - 3y = 4 and 4x - y = 18 the fifth statement: Systems A and B have different soltuoins.
Explanation:
1) The first statement: systems A and C have the same solutiotn: TRUE
The fourth statement proves that that the two systems are equivalent which means that both have the same solution.
2) The second statement: All three systems have different solutions: FALSE
The fourth statement proves that the systems A and C have same solution, so this second statement is false.
3) The third statement: Systems B and C have the same solution: FALSE
<span>You can solve the two systems and will find the solutions are different
Solution of system B.
3x - 4y = 5 y = 5x + 3
replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5
=> 3x - 20x - 12 = 5
=> - 17x = 5 + 12
=> -17x = 17
=> x = - 17 / 17
=> x = - 1
y = 5x + 3 = 5(-1) + 3 = - 5 + 3 = - 2
=> solution x = -1 and y = -2
Solution of system C.
2x - 3y = 4 12x - 3y = 54
subtract </span> 4) fourth statement: System C simplifies to <span>2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three: TRUE
Look:
Second equation of system C = 12x - 3y = 54
Divide by 3:
12x - 3y 54 ----------- = ----- 3 3
Distributive property:
12x 3y ------ - ----- = 18 3 3
4x - y = 18, which is the same second equation of system A, so the system C simplifies to the same system A, which is 2x - 3y = 4 and 4x - y = 18.
5) The fifth statement: systems A and B have different solutions: TRUE
</span><span>You can solve the two systems and will find the solutions are different
Solution of system A:
2x - 3y = 4 12x - 3y = 54 since it is equivalent to 4x - y = 18 ------------------- 12x - 2x = 54 - 4 subtracting the first equation from the secon
