Which of the following is incorrect?
1 point
The point (4, 0) lies on the graph of the linear equation 3x + 4y = 12
The linear equation 4x – y = x – 1 has unique solution
Graph of equation x=1 is a line parallel to y -axis
Graph of equation y=1 is a line parallel to x -axis
well, check them out
3*4 + 4*0 = 12 -- true
The second one simplifies to y = 3x+1, which is a line with many points (solutions) on it.
The last two are clearly true -- graph them to see.
To determine which of the following statements is incorrect, we need to analyze each statement individually.
1. The point (4, 0) lies on the graph of the linear equation 3x + 4y = 12.
To check this, substitute the x and y values of the point into the equation and see if it is satisfied:
3(4) + 4(0) = 12
12 + 0 = 12
12 = 12
Since the equation is true, this statement is correct.
2. The linear equation 4x – y = x – 1 has a unique solution.
To check this, let's simplify the equation:
4x - y = x - 1
3x + y = -1
This is a linear equation in standard form, and it represents a line. Since a line has infinitely many solutions, this statement is incorrect.
3. The graph of the equation x = 1 is a line parallel to the y-axis.
This statement is correct. The equation x = 1 represents a vertical line passing through the point (1, 0) on the x-axis. It is parallel to the y-axis because it spans the entire y-axis.
4. The graph of the equation y = 1 is a line parallel to the x-axis.
This statement is also correct. The equation y = 1 represents a horizontal line passing through the point (0, 1) on the y-axis. It is parallel to the x-axis because it spans the entire x-axis.
Therefore, the incorrect statement is: "The linear equation 4x – y = x – 1 has unique solution."