SOLUTION: this question is about how to solve equation using substitution 4x-7y=10 y=x-7 what is x and y? and question 10 ; 2x-y=23 x-9=-1 what is x and y?

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Question 177950This question is from textbook McDougal Littell Algebra 1
: this question is about how to solve equation using substitution
4x-7y=10
y=x-7
what is x and y?
and question 10 ;
2x-y=23
x-9=-1
what is x and y?
This question is from textbook McDougal Littell Algebra 1

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
I will do the first and you can do the 2nd
:
this is solving a system of equations. You are trying to find the value and values of x and y that will satisfy both equations. We are using the substitution method. This means we will isolate a variable in one of the equations(x or y-makes no difference) and take the value of that variable and plug it into the other equation.
4x-7y=10....eq 1
y=x-7.......eq 2
:
In our particular situation y is already isolated in eq 2 and its value is x-7
so we take that and plug that value into every place y occurs in eq 1 and solve for x
:
4x-7(x-7)=10.....plugged in y value of x-7(eq 1)
:
4x-7x+49=10.......distributed left side
:
-3x=-39......combined like terms on left and right
:
highlight%28x=13%29
:
now we take x's found value and plug it back into either eq 1 or 2 and solve for y. I choose eq 2
:
y=x-7
:
y=13-7=6
:
highlight%28y=6%29
:
now if you take those values they should work as solution in both equations
:
4x-7y=10....eq 1---->4(13)-7(6)=10--->52-42=10--->10=10...check
y=x-7.......eq 2---->6=13-7----------------------->6=6....check