Question

The X intercept is also considered to be the linear equation y = 0. Knowing this, do you think the number of solutions apply to all linear equations? Justify your answer. a) Yes, the number of solutions applies to all linear equations. b) No, the number of solutions only applies to specific linear equations. c) It depends on the coefficients of the linear equation. d) There is not enough information to determine.

Answer 1

The number of solutions of a linear equation is determined by the coefficients of the equation. All linear equations have one unique x-intercept - the point where the line crosses x-axis or the solution when y = 0, except in specific cases like vertical lines or coincident lines.

Step-by-step explanation:

Let's consider your question about the number of solutions applicable to all linear equations. The number of solutions of a linear equation y = mx + b can be interpreted graphically. The y-axis corresponds to y = 0 and the x-axis to x = 0. The x-intercept- the x-coordinate where the line crosses the x-axis- indicates the solution for the equation when y = 0.

All linear equations of the form y = mx + b, with m and b as constants, have only one unique solution. In specific cases, like when the equation is a vertical line or when we have infinite solutions (as in the case of coinciding lines), the standard definition might not apply. Therefore, to answer your question (c) 'It depends on the coefficients of the linear equation' would be the most appropriate.

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