Final answer:
To solve the simultaneous equations y = x² and Y = 3x - 2, you can use the substitution method. Solve one equation for a variable, substitute the expression into the other equation, simplify and solve the resulting equation to find the values.
Step-by-step explanation:
To solve the simultaneous equations y = x² and Y = 3x - 2, we can use the substitution method. We can solve one equation for a variable and substitute that expression into the other equation.
From the second equation, we can isolate x: 3x - 2 = Y. Rearranging, we get x = (Y + 2)/3.
Substitute this expression for x in the first equation: y = ((Y + 2)/3)². Simplify this equation to get a quadratic equation in terms of Y. Solve this equation to find the values of Y, and then substitute the values obtained for Y back into the second equation to find the corresponding values of x.