Final answer:
To solve the provided system of linear equations, the elimination method is used to first find the value of y, and then substitute this value back into an original equation to find x. The solution is x = 1/2 and y = -1/3.
Step-by-step explanation:
To solve the system of equations, we can use either the substitution method or the elimination method. In this case, the elimination method may be more straightforward. We have the following equations:
- 10x - 9y = 8
- 21y + 15x = 0.5
To eliminate one of the variables, multiply the first equation by 15 and the second equation by 10, so the coefficients of x will be equal.
- (15)(10x - 9y) = (15)(8)
- (10)(21y + 15x) = (10)(0.5)
Distribute and get:
- 150x - 135y = 120
- 210y + 150x = 5
Now we subtract the second equation from the first:
- (150x - 135y) - (210y + 150x) = 120 - 5
- -345y = 115
Then, solve for y:
y = -115 / 345
y = -1/3
Now that we have y, substitute it back into one of the original equations to find x:
10x - 9(-1/3) = 8
10x + 3 = 8
x = 5 / 10
x = 1/2
Therefore, the solution to the system is x = 1/2 and y = -1/3.