Final answer:
To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations by a suitable factor so that the coefficients of one variable will be opposites. In this case, we can multiply the first equation by 2 and the second equation by 3 to eliminate the x variable. After simplifying, we find that x = ±√11 and y = -4.
Step-by-step explanation:
To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations by a suitable factor so that the coefficients of one variable will be opposites. In this case, we can multiply the first equation by 2 and the second equation by 3 to eliminate the x variable.
After multiplying, we get:
6x² + 8y = 34
6x² + 15y = 6
Now, we subtract the second equation from the first equation to eliminate the x variable:
(6x² + 8y) - (6x² + 15y) = 34 - 6
-7y = 28
y = -4
Substitute this value of y back into either of the original equations to solve for x. Let's use the first equation:
3x² + 4(-4) = 17
3x² - 16 = 17
3x² = 33
x² = 11
x = ±√11
Therefore, the solution to the system of equations is x = ±√11 and y = -4.