Question 1106663: Which expression can be substituted for x in the top equation of the following system to solve the system by substitution? What is the solution?
−2x−3y=−13
x+y=6
The choices are :
1) −y+6, (5,1)
2) y+6, (-1/5 ,1/5) that's meaning 1 over neg 5,and 1 over 5
3)-3/2y+13/2 (5,1)
4) 6−y, (1,5)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equations to solve are:
−2x − 3y = −13
x + y = 6
in the second equation, solve for x to get x = -y + 6.
in the first equation, replace x with (-y + 6) to get -2(-y+6) -3y = -13.
simplify to get 2y - 12 - 3y = -13
combine like terms to get -y - 12 = -13
solve for y to get y = 1.
go back to your original equations.
they are:
−2x − 3y = −13
x + y = 6
replace y in the second equation with 1 to get x + 1 = 6
solve for x to get x = 5.
your solution is x = 5 and y = 1.
replace x with 5 and y with 1 in the first original equation to get −2(5) − 3(1) = −13
simplify to get -10 - 3 = -13 which reduces to -13 = -13 which is true.
this conforms the solution is correct.
your solution is (x,y) = (5,1).
your choices are:
1) −y+6, (5,1)
2) y+6, (-1/5 ,1/5) that's meaning 1 over neg 5,and 1 over 5
3)-3/2y+13/2 (5,1)
4) 6−y, (1,5)
eliminate selection 2 and 4 because their coordinate solution is not (5,1).
that leaves selection 1 or selection 3.
you were asked to substitute for x in the first equation.
you did that by solving for x in the second equation and then substituting for x in the first equation.
when you solved for x in the second equation, you got x = -y + 6.
you solution is therefore selection 1.
selection 1 is:
1) −y+6, (5,1)
the first part of that selection is the value that you substituted for x.
the second part of that selection is the solution in coordinate form.
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