To solve the system of linear equations by graphing, we will graph each equation on the same coordinate plane and find the point where the two lines intersect.
We can start by graphing the equation y=x+3. We can choose any values for x and solve for y to get the coordinates to plot. Let's choose x=0, x=1, and x=-1.
For x=0, y=0+3=3. So, the first point is (0,3).
For x=1, y=1+3=4. So, the second point is (1,4).
For x=-1, y=-1+3=2. So, the third point is (-1,2).
Now, let's graph the equation −4x+4y=28. To do this, we can solve the equation for y in terms of x and choose values of x to get the corresponding y values. Let's choose x=0, x=1, and x=-1.
For x=0, −4(0)+4y=28. Simplifying, we get 4y=28, which gives y=7. So, the first point is (0,7).
For x=1, −4(1)+4y=28. Simplifying, we get -4+4y=28, which gives 4y=32 and y=8. So, the second point is (1,8).
For x=-1, −4(-1)+4y=28. Simplifying, we get 4+4y=28, which gives 4y=24 and y=6. So, the third point is (-1,6).
Now, let's plot these points on the same coordinate plane and draw the lines passing through them.
- The graph of y=x+3 will have a positive slope of 1, meaning it will go upwards from left to right. It will intersect the y-axis at y=3.
- The graph of −4x+4y=28 will have a positive slope of 1, meaning it will also go upwards from left to right. It will intersect the y-axis at y=7.
The two lines will intersect at a single point, which represents the solution to the system of linear equations. We can find the coordinates of this point by finding the point where the two lines intersect on our graph. This intersection point represents the solution to the system of linear equations.
The description of the graph and the intersection point will clarify the solution to the system of linear equations.
Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations.
y=x+3
−4x+4y=28
(2 points)
1 answer
1 answer