Solve the simultaneous equations using graph method (x + y=2).(x _y=4) make y the subject of the formula for number a x+y=2

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 $-y = 4 \implies y = -4$. 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 $x + y = 2$: $3 + (-1) = 2 \implies 2 = 2$ (True) • For $x - y = 4$: $3 - (-1) = 4 \implies 3 + 1 = 4 \implies 4 = 4$ (True) Both equations are satisfied.

The solution to the simultaneous equations is: $x = 3$ $y = -1$ The solution is $\boxed{x=3, y=-1}$.

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: $y = \boxed{2 - x}$