Answer:
To solve the system of equations:
y = 3x + 5 (Equation 1)
y = 4x^2 + x (Equation 2)
We can substitute Equation 1 into Equation 2, to get:
3x + 5 = 4x^2 + x
Simplifying and rearranging, we get:
4x^2 - 2x - 5 = 0
We can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 4, b = -2, and c = -5.
Substituting these values into the formula, we get:
x = (-(-2) ± √((-2)^2 - 4(4)(-5))) / 2(4)
Simplifying, we get:
x = (2 ± √84) / 8
x ≈ 1.053 or x ≈ -1.193
Substituting each value of x into Equation 1, we can find the corresponding value of y. So, the solutions to the system of equations are:
(x, y) ≈ (1.053, 8.158) or (x, y) ≈ (-1.193, 0.384)