Final answer:
After substituting the value of x from the first equation into the second equation and simplifying, we get a quadratic equation. Solving this quadratic equation gives us two possible values for y: 3/2 and 1. Substituting these values back into the original equations, we find the solutions to be x = 2, y = 3/2, or x = 4, y = 1.
Step-by-step explanation:
To solve the simultaneous equations x + 8y = 4 and x/2 + 3/y = 13, we can use the method of substitution. To begin, let's solve the first equation for x: x = 4 - 8y. Now substitute this value of x into the second equation: (4 - 8y)/2 + 3/y = 13. Simplifying further, we get: 2 - 4y + 6/y = 13. Multiplying through by y to remove the fraction, we have 2y - 4y^2 + 6 = 13y. Rearranging the terms, we get 4y^2 - 11y + 6 = 0. Factoring this quadratic equation, we find (2y - 3)(2y - 2) = 0. This gives us two possible values for y: y = 3/2 or y = 1.
Substituting these values back into the original equations, we find that for y = 3/2, x = 2, and for y = 1, x = 4. Therefore, the solutions to the simultaneous equations are x = 2, y = 3/2 (or x = 4, y = 1).