Answer:
To solve the equation 2x + y = 7 graphically, we'll plot the equation on a Cartesian coordinate system and find the point where it intersects the axes.
First, let's rearrange the equation to solve for y:
2x + y = 7
y = 7 - 2x
Now, we'll create a table of values for x and find corresponding y values:
x y
0 7
1 5
2 3
3 1
Now, let's plot these points on the graph:
When x = 0, y = 7, so the point (0, 7) is on the graph.
When x = 1, y = 5, so the point (1, 5) is on the graph.
When x = 2, y = 3, so the point (2, 3) is on the graph.
When x = 3, y = 1, so the point (3, 1) is on the graph.
Now, let's plot these points on the graph and draw a straight line passing through them.
|
7 | *
| *
| *
| *
| *
| *
|*__________
| *
|_______________
0 1 2 3 (x)
Now, draw a straight line passing through these points. This line represents the graph of the equation 2x + y = 7.
The solution to the equation is the point where this line intersects the y-axis. In this case, it intersects the y-axis at y = 7.
So, the solution to the equation 2x + y = 7 is (0, 7).
