I need learn this math

Question

Need solving this math problem: -5x+y=-3; 3x-8y=24

   

Answer 1

So this is a system of equations. Our two equations are lines, right? Like we could plot -5x+y=-3 on a graph, then we could plot 3x-8y=24 and see whether they:

 

1)cross each other(and then figure out the x and y values by looking at the graph

2)are parallel(thus never touch)

 

or

 

3)are actually the same line

 

Luckily we don't need to graph to do this, but it's good to know we COULD do that. Instead we'll use either 'substitution' or 'elimination.'

 

Substitution is where you take one of your equations, solve for one of the variables(make it look like 'x=stuff' or 'y=stuff'), then plug that "stuff" in where the variable is in the 2nd equation. If we did that with this system, it'd look like this:

-5x+y=-3
3x-8y=24

hmm, probably should solve for y in the top equation because otherwise I'm dividing everything by -5, 3, or -8.

-5x+y=-3
+5x     +5x

y = 5x-3

Now I plug 5x - 3 in wherever I see a 'y' in the 2nd equation

3x - 8(5x - 3) = 24

this is useful because now I just have x terms in this equation. After distributing the -8 through 5x - 3 I get this:

3x - 40x + 24 = 24

-33x = 0

x = 0

now I can solve for y by plugging in my value for x into either equation. I'll pick the first one.

-5(0) + y = -3

y = -3

You could also do elimination for this problem, but substitution turned out to be the easiest.

Answer 2

I believe you want to solve this system of two linear equations.

 

From the first one,you can solve for y VERY EASILY: y = 5x-3.

 

Then you substitute this into the second equation, for y:  3x - 8(5x-3) = 24.

 

Now, distribute; you get 3x -40x + 24 = 24;  this leads to -33x = 0, and thus x = 0.

 

That means y must be -3.  I have worked this out for you to study carefully and learn to do similar problems yourself in the future.  BTW the solution is one point, with coordinates (0, -3).