# Linear Equations in Two Variables - Solutions on the Graph

Author:
Lew W. S.
What do you mean by values that satisfy an equation ? In the equation 3x + 1 = 7, x is unknown. But we can solve the unknown x The left side of the equation 3x + 1 equals to the value of 7 on the right of the equation. Only one value of x satisfies the equation, ie. if x = 2, the left side of the equation becomes 3(2) + 1 = 6 + 1 = 7 (equals the value on the right) We can also solve the equation 3x + 1 = 7 algebraically by this Subtracting 1 from both sides, 3x + 1 - 1 = 7 - 1 then 3x = 6 Dividing both sides by 3, x = 2 What about linear equations of two variables? for example 2x + y = 7 What are the values of x and y which satisfy the equation above? If x = 1, and y = 5 the left side of the equation becomes 2(1) + 5 = 7 (equals the value on the right of the equation. If x = 2, and y = 3 the left side of the equation becomes 2(2) + 3 = 7 (again equals value on the right of equation) If x = 1.5 and y = 4 the left side of the equation is 2(1.5) + 4 = 7 (again equals value on the right of equation) In other words the pairs of values x =1 and y = 5, x = 2 and y = 3, x = 1.5 and y = 4 are possible solutions to the unknowns x and y since they satisfy the equation 2x + y = 7. In fact, there are countless number of possible pairs of x and y values that satisfy the equation. With this applet below, find the x and y values that satisfy equations of lines appearing below. How do the pairs of x and y values relate to the equation of the line?

What do the x and y coordinates of all the points on the line have to do with the linear equation in two variables ?