Final answer:
To find the solutions of the given system of equations using the elimination method.
Step-by-step explanation:
The given system of equations is:
{x²-2y=1
{x²+5y=29
To solve this system using the elimination method, we need to eliminate one of the variables so that we can solve for the other variable. In this case, we can eliminate the variable x by subtracting the equations:
(x²+5y) - (x²-2y) = 29 - 1
7y = 28
y = 4
Substitute the value of y back into one of the original equations to solve for x:
x²+5(4) = 29
x² = 9
x = ±3
Therefore, the solutions to the system of equations are (x, y) = (-3, 4) and (3, 4).