SOLUTION: 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

Algebra.Com
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.






RELATED QUESTIONS

which expression can be substituted for x in the top equation of the system below to... (answered by stanbon)
Which expression can be substituted for x in the top equation of the system below to... (answered by algebrahouse.com)
*You want to get rid of the x by elimination in the system below. 3x + 4y = 7 4x – 2y (answered by mananth)
Which expression can be substituted for y in the top equation of the following system to (answered by josgarithmetic)
Which expression can be substituted for y in the top equation of the system to solve... (answered by josgarithmetic)
Which expression can be substituted for y in the top equation of the following system to (answered by Alan3354)
Which expression can be substituted for x in the top equation of the system to solve the... (answered by addingup)
6. Which expression can be substituted for y in the bottom equation of the system... (answered by rfer)
Considering these two equations: y-3x=4 3y+2x=1 Which expression can be... (answered by Fombitz)