Final answer:
To solve the system of linear equations 1.5x - 9y = -21 and -1.5x - 3y = 9 by elimination, we can add the two equations together to eliminate the x variable and solve for y. Then, substitute the value of y back into one of the equations to solve for x. The solution is x = -8 and y = 1.
Step-by-step explanation:
To solve the system of linear equations by elimination, we want to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate the x variable by adding the two equations together. When we do this, the x variable cancels out:
1.5x - 9y + (-1.5x - 3y) = -21 + 9
-12y = -12
Now we can solve for y:
y = -12 / -12 = 1
Next, we substitute the value of y back into one of the original equations to solve for x:
1.5x - 9(1) = -21
1.5x - 9 = -21
1.5x = -12
x = -12 / 1.5 = -8
Therefore, the solution to the system of linear equations is x = -8 and y = 1.