solve by graphing:
x+y=1
2x+y=0
I know that the answer is (-1,2)and i know how to mark the spot but can you explain how to draw the lines because i cant figure out the directions it goes in.
To graphing a straight line:
1. Draw your axes.
2. Set x=0 in your equation to get the y-intercept:
x + y = 1
0 + y = 1
y = 1
so we have one point: (0,1)
3. Set y=0 in your equation to get the x-intercept:
x + y = 1
x + 0 = 1
x = 1
so we have a second point: (1.0)
4. Mark the two points on your graph, and use a ruler to draw the straight line that goes through them.
I usually go for the x- and y-intercepts as my points, but any two points will do. Sometimes you can't use two intercepts, as in your second equation:
2x + y = 0
2(0) + y = 0
y = 0
So the origin (0.0) is on this line.
The x- and y-intercepts are the same.
We need another point. No problem; just set x = anything else, for example 3:
2x + y = 0
2*3 + y = 0
y = -6
So we can use the point (3, -6) as our second point. Mark it, and get out the ruler again to draw a straight line through (3, -6) and the origin.
The two lines should meet at the point you expect.
Certainly! To graph the lines, you need to identify two points on each line and then connect them to form the line.
Let's start with the first equation, x + y = 1. To find two points on this line, you can choose any values for x and solve for y. For example, you could set x = 0, which gives y = 1. The first point is (0, 1).
For the second point, you can set y = 0 and solve for x. If you plug in y = 0 into the equation x + y = 1, you get x + 0 = 1. Therefore, x = 1. The second point is (1, 0).
Now, let's move on to the second equation, 2x + y = 0. Again, choose two values for x and solve for y. For simplicity, let's choose x = 0. Substituting this into the equation gives us 2(0) + y = 0, which simplifies to y = 0. The first point is (0, 0).
For the second point, we can set x = 1 and solve for y. Substituting x = 1 into the equation 2x + y = 0 gives us 2(1) + y = 0. Simplifying this equation, we have 2 + y = 0, which gives y = -2. The second point is (1, -2).
To graph these lines, plot the two points for each equation on a coordinate plane and draw a straight line passing through them. You can use a ruler or graphing software for accuracy. After drawing both lines, the point where they intersect is the solution to the system of equations: (-1, 2).
Remember, if you're having trouble determining the direction of the lines, you can also calculate additional points to verify your graph.