Question

To solve the system of linear equations. {(x-2y=5),(2x-3y=12):} (x,y)=(1)

Answer 1

The solution to the system of linear equations x-2y=5 and 2x-3y=12 is found by using the elimination method. Multiplying the first equation by 2, then subtracting it from the second equation yields y = 2, and substituting this into the first equation gives x = 9. Hence, the solution is (9,2).

Step-by-step explanation:

To solve the system of linear equations consisting of (x-2y=5) and (2x-3y=12), we can use either the substitution method, the elimination method, or the graphical method. Since we aren't provided with a preferred method, I will demonstrate solving this system using the elimination method, which is often efficient for such problems.

1. Multiply the first equation by 2 to align the x coefficients: 2(x - 2y) = 2(5), which simplifies to 2x - 4y = 10.
2. Next, subtract the first equation from the second one to eliminate the x variable: (2x - 3y) - (2x - 4y) = 12 - 10, yielding y = 2.
3. To find the value of x, we substitute y = 2 back into one of the original equations, such as x - 2(2) = 5. Simplifying this gives us x = 9.

Therefore, the solution to the system of linear equations is the point (x, y) where x = 9 and y = 2.