9514 1404 393
Answer:
M R T V B K
Explanation:
From left to right the solutions are ...
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B: equating expressions for y
-2x = x -3 ⇒ 3 = 3x ⇒ x = 1
R: given
x = -2
V: filling in for y
4x +5(2) = 10 ⇒ x = 0
T: subtracting the first from twice the second
2(3x +y) -(-3x +2y) = 2(0) -9 ⇒ 9x = -9 ⇒ x = -1
K: adding the two equations
(2x +y) +(3x -y) = (7) +(3) ⇒ 5x = 10 ⇒ x = 2
M: equating expressions for y
x -2 = 1/3x -6 ⇒ 2/3x = -4 ⇒ x = -6
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The solutions in order least to greatest are ...
-6 (M), -2 (R), -1 (T), 0 (V), 1 (B), 2(K)
The passcode is MRTVBK.
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Additional comment
In several cases, there are variables and constants on both sides of the equal sign. The solution method is to identify the smallest variable coefficient, and add the opposite of that term. Also added at the same time is the opposite of the constant term on the other side of the equal sign. The net effect is to put the variable on one side and the constant on the other side. Then the equation is divided by the coefficient of the variable.
For example, in the first equation, -2x is the variable term with the smallest coefficient. -3 is the constant on the other side of the equation. To get from the initial expression to the next, we add 2x+3 to both sides of the equation.