Solve x=3y+11, 2x+5y=0 by using substition or elimination?

Question

is it:
a.(5,-2)
b.(2,-5)
c.(-2,5)
d.(-5,2)

Answer 1

By substitution:

Basically you substitute each of the combinations into the 2 equations and see if they work out for both. Since this is a mutliple choice there is only one correct answer. Trial and error is the only way for substituting.
For example in choice A, (5,-2) means x= 5 and y= -2. Substituting them in you get (5)=3(-2)+11 and 2(5)+5(-2)=0. Solve it and now you arrive with 5=5 and 0=0 respectively. Fortunately choice A already works out that means it is the correct answer which worked on the first try.


By elimination:

Convert them into the same form, in this case I will use the form of the first equation. By that I mean rearranging the second equation to make it appear as "x=(number)y+(number)". For the second equation, 3x+5y=0 turns into x = (-5/2)y+(0). Comparing this form of the second equation to x=3y+11 like so: 1st equation: x= (3) y + (11)
2nd equation: x=(-5/2)y + (0)
By elimination, it means minusing or adding the equations term by term whenever there is a set of terms with equivilant coefficients. In this case, the 2 "x" in both equations happen to be multiplying by an invisible 1. Therefore you proceed to minusing the 1st equation by the 2nd equation vertically like so:

1st equation: x= (3) y + (11)
2ns equaiton: - x=(-5/2)y + (0)
x - x = 0
(3)y - (-5/2)y = (11/2)y
(11) - (0) = 11
the 2 equations ends up like this after minusing the terms:

0=(11/2)y+(11)
Now solve the equation for y, keep in mind a point is in the form of (x,y). It turns out y=(-2),to prove it just substitute it in: 0=(11/2)(-2)+(11). Now that you know y=(-2),substitute in -2 as y in one of the 2 equations given by the question to find the value of x. Lets use the 1st equation: x=3(-2)+11. It turns out x=5. We can also do this to the 2nd equation: 2x+5(-2)=0, which also ends up telling us x=5. Therefore the answer is x=5,y=-2. In the form of (x,y), it is (5,-2).

The answers derived from the substitution and elimination are both (5,-2). It means that you can come up with the answer from using both methods. That is why the problem gave you the choice of 2 methods since they come up with the equivilant answer.

Hope this not only answers your math problem, but also help you understand on how to solve this kind of problem in the future when you happen to encounter a similar question like this one.

Answer 2

Easiest way is to use substitution. Since you know that x = 3y + 11, then you can substitute into the other equation: 2(3y + 11) + 5y = 0. Use Distributive Property: 2(3y) + 2(11) + 5y = 0 Simplify: 6y +22 + 5y = 0 Combine like terms: 11y + 22 = 0 Subtract 22 from both sides: 11y = -22 Divide 11 from both sides: y = -2 Plug -2 in for y in the equation x = 3y + 11: x = 3(-2) + 11 Solve: x = -6 + 11 = 5 So, x = 5 and y = -2

Answer 3

The above equations can be re-written as

x-3y =11 --- (1)
2x+5y=0 --- (2)

Multiply eqn (1) by 5 and eqn (2) by 3 and add

5x-15y=55
6x+15y =0

which implies 11x=55 => x = 5

Therefore y = -2

Hence the answer is (a)

Answer 4

if you were to use substitution:
2(3y + 11) + 5y = 0
6y + 22 + 5y = 0
11y + 22 = 0
y = -2

x = 3y + 11
x = 3(-2) + 11
x = 5

Answer 5

6y + 22 + 5y = 0
11y = - 22
y = - 2
x = - 6 + 11 = 5
x = 5, y = - 2
Option a

Answer 6

2(3y+11)+5y=0
6y+22+5y=0
11y+22=0
11y=-22
y=-2

x=3(-2)+11

answer is c. (-2,5)
x=-6+11
x=5

Answer 7

seriously..do your owm homework.

but its..
2(3y+11)+5y=0
6y+22+5y=0
11y=-22
y=-2
x=3(-2)+11
x=-6+11
x=5
a. (5,-2)

Answer 8

Substitution

Answer 9

I agree with sandysurd and go with answer A