SOLUTION: Can someone explain the step to solve a Linear Systems equation like this on? I don't understand any of this. Thank you. {{{2x+3y=1}}} {{{ x- y=3}}}

Algebra ->  College  -> Linear Algebra -> SOLUTION: Can someone explain the step to solve a Linear Systems equation like this on? I don't understand any of this. Thank you. {{{2x+3y=1}}} {{{ x- y=3}}}       Log On


   

Question 20088: Can someone explain the step to solve a Linear Systems equation like this on? I don't understand any of this. Thank you.
2x%2B3y=1
++x-++y=3
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You are starting with two equations with two unknowns (variables x and y).
The basic idea is to reduce this system of linear equations to one equation with one unknown. It doesn't matter which of the two original unknown variables you end up with in you single equation because, eventually, you will be solving for the other unknown.
Here's how it goes, starting with your two equations:
2x+%2B+3y+=+1 and
x+-+y+=+3 Solve this equation for x: x+=+y+%2B+3 and substitute this x into the first equation. This will result in one equation with one unknown, which you can readily solve.
2%28y+%2B+3%29+%2B+3y+=+1 Simplify and solve for y.
2y+%2B+6+%2B+3y+=+1
5y+%2B+6+=+1 Subtract 6 from both sides of the equation.
5y+=+-5 Divide both sides by 5.
y+=+-1 Now that you have the value for y, you can substitute this into either of the two original equations and solve for x. Let's take the second equation.
x+-+y+=+3 Substitute y = -1
x+-+%28-1%29+=+3 Simplify.
x+%2B+1+=+3 Subtract 1 from both sides.
x+=+2
The solution to this system of linear equations is the point: (2, -1)
This is the point at which the two lines, represented by the two linear equations, intersect.
Let's take a look at the graph of this system:
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-%282%2F3%29x%2B1%2F3%2Cx-3%29