Final answer:
To solve the system of equations, you can use either the substitution or elimination method. In this case, let's use the elimination method. Multiply the second equation by 3 and subtract it from the first equation to eliminate the x variable. Then, solve for y and substitute the value of y back into one of the original equations to solve for x. The solution to the system of equations is x = 7 and y = 2.
Step-by-step explanation:
To solve the system of equations:
3x - 2y = 17
x - 3y = 1
You can use either substitution or elimination method. Let's use the elimination method:
Multiply the second equation by 3:
3(x - 3y) = 3(1)
3x - 9y = 3
Now subtract this equation from the first equation:
3x - 2y - (3x - 9y) = 17 - 3
3x - 2y - 3x + 9y = 14
7y = 14
Simplify:
y = 2
Substitute the value of y back into one of the original equations:
x - 3(2) = 1
x - 6 = 1
x = 7
So the solution to the system of equations is x = 7 and y = 2.