This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's break this down into two parts. Part 1: Solve the simultaneous equations using the graph method The given equations are: 1) x + y = 2 2) x - y = 4 Step 1: Find two points for the first equation, x + y = 2. • If x = 0, then y = 2. Point: (0, 2). • If y = 0, then x = 2. Point: (2, 0). These points define the first line. Step 2: Find two points for the second equation, x - y = 4. • If x = 0, then -y = 4 y = -4. Point: (0, -4). • If y = 0, then x = 4. Point: (4, 0). These points define the second line. Step 3: Identify the intersection point. When these two lines are plotted on a graph, their intersection point is the solution. From the graph, the lines intersect at (3, -1). Step 4: Verify the solution. Substitute x=3 and y=-1 into both original equations: • For x + y = 2: 3 + (-1) = 2 2 = 2 (True) • For x - y = 4: 3 - (-1) = 4 3 + 1 = 4 4 = 4 (True) Both equations are satisfied. The solution to the simultaneous equations is: x = 3 y = -1 The solution is x=3, y=-1. Part 2: Make y the subject of the formula for x+y=2 Step 1: Start with the given equation. x + y = 2 Step 2: Subtract x from both sides of the equation to isolate y. y = 2 - x So, y as the subject of the formula is: y = 2 - x Drop the next question.