Solve the system by graphing.
x + y = 4
–x + y = 2
confused where do i start do i need to solve for x and find points
I'll bet that after doing a few like this you would be able to do this one in your head.
just add then up. The x's will cancel and you will have 2y = 6
so dividing by 2 gives y = 3
so mentally replace the y with 3 in the first equation and you are left with
x + 3 = 4
using just good ol' common sense will give you x = 1
To solve the system of equations by graphing, you need to plot the equations on a graph and find their point of intersection. Here's how you can do it:
1. Start by rearranging both equations in "y = mx + b" form, where m is the slope and b is the y-intercept.
Equation 1: x + y = 4 -> y = -x + 4
Equation 2: -x + y = 2 -> y = x + 2
2. Now, choose some x-values and plug them into each equation to find the corresponding y-values. To keep things simple, you can choose small integers or fractions.
For Equation 1:
- When x = 0, y = -0 + 4 = 4 (point A: (0, 4))
- When x = 2, y = -2 + 4 = 2 (point B: (2, 2))
For Equation 2:
- When x = 0, y = 0 + 2 = 2 (point C: (0, 2))
- When x = 2, y = 2 + 2 = 4 (point D: (2, 4))
3. Plot these points on a graph. Point A is (0, 4), point B is (2, 2), point C is (0, 2), and point D is (2, 4).
4. Draw a straight line passing through point A and point B. This represents the graph of Equation 1.
5. Draw a straight line passing through point C and point D. This represents the graph of Equation 2.
6. The point at which these two lines intersect is the solution to the system of equations. In this case, it is the point (1, 3).
Therefore, the system of equations x + y = 4 and -x + y = 2 is solved by graphing as (x, y) = (1, 3).