Answer:
x = 1/13 and y = 37/13.
Explanation:
To solve the system of equations:
2x + y = 3 ...(1)
4x^2 - y^2 + 2x + 3y = 16 ...(2)
We can use the method of substitution or elimination.
Let's start by using the substitution method. Rearrange equation (1) to solve for y:
y = 3 - 2x
Now substitute this expression for y in equation (2):
4x^2 - (3 - 2x)^2 + 2x + 3(3 - 2x) = 16
Expand and simplify the equation:
4x^2 - (9 - 12x + 4x^2) + 2x + 9 - 6x = 16
Combine like terms:
4x^2 - 9 + 12x - 4x^2 + 2x + 9 - 6x = 16
Simplify further:
4x + x - 6x - 12x = 16 - 9 - 9 + 6
Combine like terms:
-13x = -1
Divide both sides of the equation by -13:
x = 1/13
Now substitute this value of x back into equation (1) to solve for y:
2(1/13) + y = 3
Multiply through by 13 to eliminate the fraction:
2 + 13y = 39
Subtract 2 from both sides:
13y = 37
Divide both sides by 13:
y = 37/13
Therefore, the solution to the system of equations is:
x = 1/13
y = 37/13
So, the values of x and y that satisfy both equations are x = 1/13 and y = 37/13.