I'm having trouble learning "Solving systems of equations by graphing". Can you show me how to do the following problem?
X + Y = 2
X - Y = 0
Solve the system.
I know it should be easy, but for some reason I just don't see it.
Draw a graph showing the two straight lines defined by those equations. They will intersect at a point (x,y), and that is the solution.
X-Y = 0 is a 45 degree line (slope = 1) through the origin. The other line has a slope of -1 and passes through the point (0,2).
Pick any two points on each of the equations.
For your equations that should be quite easy, you should be able to do so by just inspection.
e.g. for the first one (2,0) and (0,2) would work, I used the intercepts.
Join these two points and draw a straight line.
for the second one, how about (0,0) and (5,5) ?
Join these two points and draw a straight line.
Where these two lines intersect becomes the solution to the system.
(looks like (1,1) is the intersection point)
Some calculators are graphing calculators but I don't know how to use them. If you have one, read the instructions. For doing this manually,
make a table with two columns. The dots are to control spacing; they have no meaning mathematically.
X......Y
Using the first equation, let X = 0 and solve for Y. Y= 2 so write 0 in the X column and 2 in the Y column. Then give X a value of 1 and solve for Y. Y = 1. Place 1 in the X column and 1 in the Y column. Technically you can quit here since two points define a straight line; however, I often make little arithmetic errors so I usually plot a third point to make sure it is on the same line. So I usually give Y = 0 and solve for X. X = 2. Now plot those three points on a sheet of graph paper and draw the line.
Do the same thing for the second equation and plot those points on the same sheet and draw the line. The solution of the set of equation is where the two straight lines intersect. If I didn't goof, they should intersect at X=1, Y = 1 but check my work.
Of course! I'm here to help, even if it means cracking a few jokes along the way.
To solve the system of equations by graphing, let's start by rewriting the equations in slope-intercept form (just for fun):
1) X + Y = 2
Y = -X + 2
2) X - Y = 0
Y = X
Now, let's plot these two lines on a graph. Are you ready for some arts and crafts?
Plot the first equation: Y = -X + 2
To get started, put on your imaginary painter's beret and pretend you're Bob Ross painting happy little lines.
Plot a point at the y-intercept, which is 2. Since the slope is -1 (the negative coefficient of X), this means that for each unit you move to the right, you'll move down one unit. So, starting from our first point, draw a nice sloping line downward. Voila!
Now let's plot the second equation: Y = X
This time, we'll use an imaginary knitting needle to stitch the line on our graph. Since the y-intercept is 0, we'll start at the origin (0, 0). For each step to the right, take a step upward. Easy peasy!
Now, take a step back and admire your masterpiece. If you've followed my artistic instructions, you should have two lines intersecting somewhere on your graph.
The point where the lines intersect represents the solution to the system of equations. So, take a moment to appreciate the beauty of this intersection.
In this case, the lines intersect at the point (1, 1). So, solving the system, X = 1 and Y = 1.
Congratulations! You've successfully solved the system of equations. Give yourself a round of applause. And remember, when in doubt, just paint your way to math success.
Sure, I can help you with solving this system of equations by graphing.
To graph the first equation, X + Y = 2, we can rearrange it to solve for Y: Y = 2 - X. This equation represents a straight line, with the slope of -1 (because the coefficient of X is -1) and the y-intercept of 2.
For the second equation, X - Y = 0, we can rearrange it to solve for Y: Y = X. This equation also represents a straight line with a slope of 1 and a y-intercept of 0.
Now, to graph these equations, we will plot a few points to create the lines. Let's choose a few values for X and calculate the corresponding Y values for each equation:
For the first equation, let's choose X = 0. Plugging that into the equation Y = 2 - X, we get Y = 2 - 0 = 2. So we have the point (0, 2).
For the second equation, let's choose X = 0 as well. Plugging that into the equation Y = X, we get Y = 0. So we have the point (0, 0).
Now, let's choose another value for X for each equation:
For the first equation, let's choose X = 2. Plugging that into the equation Y = 2 - X, we get Y = 2 - 2 = 0. So we have the point (2, 0).
For the second equation, let's choose X = 2 as well. Plugging that into the equation Y = X, we get Y = 2. So we have the point (2, 2).
We can now plot these points on a graph and connect them to form the lines.
Next, we need to find the point where the two lines intersect. This point represents the solution to the system of equations.
By looking at the graph, we can see that the two lines intersect at the point (1, 1). This means that the solution to the system of equations is X = 1 and Y = 1.
So, the solution to the system of equations X + Y = 2 and X - Y = 0 is X = 1 and Y = 1.
I hope this step-by-step explanation helps you understand how to solve systems of equations by graphing!