Final answer:
The simultaneous equations y = x - 2 and y = 3x + 5 are solved by equating the two expressions for y and finding that x = -3.5 and y = -5.5.
Step-by-step explanation:
To solve the simultaneous equations y=x-2 and y=3x+5, we need to find a common solution for x and y that satisfies both equations simultaneously.
First, we can equate the two expressions for y since they are equal to the same variable: x - 2 = 3x + 5.
Next, we solve for x by rearranging the terms: x - 3x = 5 + 2 which simplifies to -2x = 7. Then we divide both sides by -2 to find x: x = -7/2 or x = -3.5.
Now, we can substitute x back into one of the original equations to find y. Using y = x - 2: y = -3.5 - 2, which gives us y = -5.5.
The solution to the simultaneous equations is x = -3.5 and y = -5.5. We have determined the values for both unknowns using algebraic steps and substitution.