Solve the system of equations by graphing.

Question

X = 4
Y = 2x - 3

Answer 1

To graph this system of equations, we will plot the two equations on a coordinate plane.

The first equation, x = 4, is a vertical line passing through the x-coordinate 4.

The second equation, y = 2x - 3, is a linear equation representing a straight line with a slope of 2 and a y-intercept of -3.

To graph it, we can choose a few different x-values, calculate the corresponding y-values using the equation, and plot the points.

Let's choose x = 0:
y = 2(0) - 3
y = -3
So one point is (0, -3).

Let's choose x = 2:
y = 2(2) - 3
y = 1
So another point is (2, 1).

Let's choose x = 6:
y = 2(6) - 3
y = 9
So another point is (6, 9).

Plotting these three points on the coordinate plane, we can see that the line passes through them and extends infinitely in both directions:

x-axis: -10 -5 0 5 10
y-axis:
|
-10 |
-5 |
0 | ●
5 |
10 |
|

The line passes through the points (0, -3), (2, 1), and (6, 9).

Now, let's plot the vertical line x = 4:

x-axis: -10 -5 0 5 10
y-axis:
|
-10 |
-5 |
0 |
5 |
10 |
|
●

The vertical line passes through the point (4, 0).

The point where these two lines intersect is the solution to the system of equations.

However, we can see that the lines do not intersect on the graph. This means that there is no solution to the system of equations.