Solve the simultaneous equation using graph method. x + y = 2, x - y = 4

To solve the simultaneous equations using the graph method, we need to plot each equation as a line and find their intersection point.

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 $0 + y = 2 \implies y = 2$. So, point is $(0, 2)$. • If $y = 0$, then $x + 0 = 2 \implies x = 2$. So, point is $(2, 0)$. Plot these points and draw a line through them.

Step 2: Find two points for the second equation, $x - y = 4$. • If $x = 0$, then $0 - y = 4 \implies y = -4$. So, point is $(0, -4)$. • If $y = 0$, then $x - 0 = 4 \implies x = 4$. So, point is $(4, 0)$. Plot these points and draw a line through them on the same graph.

Step 3: Identify the intersection point. The point where the two lines intersect on the graph is the solution to the simultaneous equations. From the graph provided, the lines intersect at the point $(3, -1)$.

To verify: For $x=3, y=-1$: Equation 1: $3 + (-1) = 2$ (True) Equation 2: $3 - (-1) = 4$ (True)

The solution is the coordinates of the intersection point. $x = 3$ $y = -1$

The solution is $\boxed{x=3, y=-1}$.