Solve simultaneous equations x + y = 3 and -3x + 5y = 7

The first equation can be multiplied by 3 to give 3x + 3y = 9. Then these two equations can be added by summing both left hand sides and both right hand sides to obtain the new equation 3x + 3y - 3x + 5y = 9 + 7. Now 3x and -3x can be cancelled out and 3y + 5y simplified to 8y which gives 8y = 16. Dividing both sides by 8 gives y = 2.

To obtain x, value of y = 2 can be substituted into any equation, preferably, the simpler one. Thus, x + 2 = 3 and x = 1. Therefore, the final answer is x = 1, y = 2.