Question

Graph and solve the system Y=-3x+3 Y=2x-7

Answer 1

An equation of the form y=ax+b, where a and b are constants; y and x are variable, is called a linear equation.

They are called "linear" because if we draw all the solutions of such an equation, they form a line. 

This also means that it is enough to:
 
1. find to solutions 
2. plot them on the coordinate axis
3.join those 2 points

and all the solutions of the equation y=ax+b will be on that line.


Thus, to draw line y=-3x+3

let x=0, then y=3, so one solution is (0, 3)

let y=0, then x=1 so a second solution is (1, 0)

(remark we can pick x or y to be any value, then solve for the other)


to draw the second line y=2x-7

let x=0, then y=-7
let x=3, then y=-1


plot these points and join them as shown in the picture.


The solution of the system is the point where the lines intersect, which is
 (2, -3)

Answer 2

2x-7=-3x+3 plus 3x+7
2x-7+3x+7=-3x+3+3x+7
5x=10 division by 5
5x/5=10/5
x=2
y=2x-7
y=2.2-7
y=4-7
y=-3
thats means x=2, y= -3
(2,-3)