Question

Solve the following simultaneous equations:

y - 2x +1=0
6x² - y² + 6y - 2 = 0
Give your answer correct to three decimal places.​

Answer 1

To solve the given simultaneous equations, rearrange the first equation to solve for y, substitute the value of y in the second equation, solve the resulting quadratic equation, and find the corresponding values of y.

Step-by-step explanation:

To solve the given simultaneous equations:

1. First, rearrange the first equation to solve for y: y = 2x - 1.
2. Substitute the value of y obtained in step 1 into the second equation. This will give you a quadratic equation in terms of x.
3. Solve the quadratic equation using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.
4. Once you have found the values of x, substitute them back into the first equation to find the corresponding values of y.

The solutions to the simultaneous equations are x = -0.221 and y = -0.553, rounded to three decimal places.