Final answer:
To solve the simultaneous equations 7x - 3y = 15 and 2x + 3y = 12, use the method of elimination. Add the equations to cancel out the y-terms, then solve for x and substitute to solve for y. The solutions are x = 3 and y = 2.
Step-by-step explanation:
To solve the simultaneous equations 7x - 3y = 15 and 2x + 3y = 12, we can use the method of elimination. We'll add the two equations together to cancel out the y-terms. Adding the left sides, we have 7x - 3y + 2x + 3y = 15 + 12, which simplifies to 9x = 27. Dividing both sides by 9, we find that x = 3. Now we can substitute this value of x into either equation to find y. Let's use the second equation, 2x + 3y = 12. Substituting x = 3, we get 2(3) + 3y = 12. Simplifying, we have 6 + 3y = 12. Subtracting 6 from both sides, we find 3y = 6. Dividing both sides by 3, we get y = 2. So the solutions to the simultaneous equations are x = 3 and y = 2.