SOLUTION: y=5x-13 5x+2y=19 how can I solve this I couldnt find substition/systems which is what this problem is

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Question 1206950: y=5x-13
5x+2y=19
how can I solve this
I couldnt find substition/systems which is what this problem is
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
y=5x-13
5x+2y=19
how can I solve this
I couldnt find substition/systems which is what this problem is
~~~~~~~~~~~~~~~~~~~~~~~~ 

You have a system of two equations in two unknowns.

First equation expresses y as a linear function of x.
In other words, first equation is just ready to make a substitution.


So, we apply the substitution method and replace y in the second equation
by its expression from first equation.  We get single equation for x then

    5x + 2*(5x-13) = 19.


Simplify and find x

    5x + 10x - 26 = 19

    5x + 10x = 19 + 26

       15x   =    45

         x   =    45/15 = 3.


So, x is just found.

To find y, substitute this value of x into very first equation

    y = 5x - 13 = 5*3-13 = 15-13 = 2.


ANSWER.  The solution is  x= 3, y= 2.

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I agree with the other tutor on the steps and final answer she wrote out. There's not much for me to add other than to think of "substitution" as in a "substitute teacher".

The substitute teacher is a temporary replacement for your original teacher until she or he gets back.
In this case, 5x-13 substitutes in for y, since both are equivalent.
That's how we go from 5x+2y = 19 to 5x+2(5x-13) = 19

It might help to color code things like so
5x+2y = 19
5x+2( y ) = 19
5x+2( 5x-13 ) = 19
which may illustrate the substitution process a bit better.
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