Question

Which description best describes the solution to the following system of equations? y = –2x + 9 y = –x + 8 Lines y = –2x + 9 and y = –x + 8 intersect the x-axis. Lines y = –2x + 9 and y = –x + 8 intersect the y-axis. Line y = –2x + 9 intersects the line y = –x + 8. Line y = –2x + 9 intersects the origin.

Answer 1

The equation $y = -2x + 9$ represents a line, and so does the equation $y=-x+8$

This means that every point whose coordinates $(x,y)$ satisfy either of the two equations lies on that particular line

For example, point $(10,-11)$ belongs to the first line, because $-11 = -2\cdot 10 + 9$, and similarly the point $(3,5)$ belongs to the second line, because $5 = -3+8$

The solution of a system is a point $(x,y)$ whose coordinates satisfy both equations. This means, as we just saw, that this point lies on both lines.

So, the solution of a linear system is the point of intersection between the two lines.