SOLUTION: System of Linear Equations
Read and solve for the values of the unknown using the suggested method.
show the solutions.
5.By graphical method:
2x - y = 2
4x - 2y = 4
Question 1172190: System of Linear Equations
Read and solve for the values of the unknown using the suggested method.
show the solutions.
5.By graphical method:
2x - y = 2
4x - 2y = 4 Found 2 solutions by Alan3354, Theo:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Graphing a straight line requires 2 points.
Pick 2 values for x and find y.
Plot the points.
Draw a line thru them.
you can see from the graph that the equations are identical, meaning they makle the same line on the graph.
this can also be seen by converting each eqution to slope intercept form and simplifying it.
2x - y = 2 is converted to slope intercept form as follows:
add y to both sides of the equation and subtract 2 from both sides of the equation and switch sides to get y = 2x - 2.
4x - 2y = 4 is converted to slope intercept form as follows:
add 2y to both dies of the equation and subtract 4 from both sides of the equation to get and switch sides to get 2y = 4x - 4
simplify by dividing both sides of the equation by 2 to get y = 2x - 2.
you could also see this in the standard form of each eqution because one of the equations was an exact multiple of the other.
2x - y = 2 multiplied by 2 on both sides of the equation yields 4x - 2y = 4.
if you were to solve these 2 equations simultaneously, you would do the following.
start with:
2x - y = 2
4x - 2y = 4
multiply both sides of the first equation by 2 and leave the second equation as is to get:
4x - 2y = 4
4x - 2y = 4
subtract the second equation from the first to get:
0 - 0 = 0
simplify to get:
0 = 0
all the variables dropped out and the equation is still true.
this indicates the 2 equations are identical.
since the equations are identical, there is an infinite number of solutions common to both equations.
you see that on the graph because both equations make the same line on the graph.
