can u define (equations of line and solving systems of equations)??? and???

Question

give example for each one ??


thanks

Answer 1

y = mx + b is the general formula for a line where m is the slope, b is the y-intercept and (x, y) is the point on the line.

For example, y = 4x + 2 has a slope of 4, it would cross the y-axis at y = 2 and any pair of numbers (x, y) that obeys the equality would be a point on the line; e.g., (1, 6).

A system of equations usually refers to several equation with as many unknown variables; manipulating these equations will allow you to solve for the unknown variables. Here's an example:

y = x + 2
3y = x + 16

I can substitute x + 2 for y in the second equation thus giving me 3 (x + 2) = x + 16. This becomes:

3x + 6 = x + 16
2x + 6 = 16
2x = 10
x = 5.

Answer 2

An equation of a line is an equation in 2 or more variables that contains all the points on that line. For example,
5x+2y=52 describes a line in Cartesian coordinates. If you plug in 5 for x, then y must equal 13.5, and (5,13.5) is a point on that line. (10,1) is another point on that line, (1,23.5) is a third, and so on.

Solving a system of equations is to find a common solution to every equation in the system. For example, take the two equations,
2x + 5y =0
3x + 2y =1
which is equivalent to:
6x + 15y = 0
6x + 4y = 2
A common solution would be
11y = -2, or y= (-)2/11. Plugging y= (-2)/11 back into either:
2x + 5y =0
3x + 2y =1
gives the same answer, x= 5/11. The (x,y) set (5/11, (-)2/11) solves both equations at the same time, so it is said to be a solution to that system of equations.