Final answer:
To solve the given system of equations, express x in terms of y from the second equation and substitute into the first, then solve for y and finally for x, ensuring accuracy through careful checking at each step.
Step-by-step explanation:
To solve the simultaneous equations x²-4y²=5 and 3x+4y=13 algebraically, we need to follow several steps. Firstly, from the second equation we can express x in terms of y:
3x = 13 - 4y ⇒ x = ⅓(13 - 4y)
Now, we substitute this expression for x in the first equation:
x² - 4y² = 5 ⇒ (⅓(13 - 4y))² - 4y² = 5
Upon expanding and simplifying, we'll find a value for y and then substitute that back into the expression for x to find the corresponding x value. We will follow the typical algebraic steps such as expanding the brackets, simplifying, and solving the resulting quadratic equation. Because the steps are sequential and dependent on the preceding one, accuracy, careful checking, and rechecking are required at each stage.
Once we have y, we can plug it into the second equation to find the corresponding value of x, completing the solution of the system.