Solve using the substitution method?
Topic: Solve using the substitution method?
June 16, 2019 / By Christabelle Question:
These are two problems.
Best Answers: Solve using the substitution method?
Aura | 1 day ago
Solve for Y on the bottom one, circle it and draw an arrow to the Y on the top one. Then substitute it where there was a Y. You now only have to solve for one variable just combine like terms and solve for X. You've now found both X & Y
👍 150 | 👎 1
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Originally Answered: Solve by the substitution method?
First, solve for y. You can use either equation, but the second one is easier (just add 7x to both sides to get y = 7x + 40)
Then, whenever you see y, substitute 7x + 40. So You have 4x + 3(7x + 40) = -35
4x + 21x + 120 = -35
25x + 120 = -35
25x = -155
x = -6.25
Then, substitute to get y.
y = 7(-6.25) + 40
y = -43.75 + 40
y = -3.75
I hope this information was very helpful.
You need to get a variable (letter) on one side by itself.
So in problem 1. you have x + y = 6. So subtract y from both sides and you get x = (6-y) Now plug that value in to the second equation.
x- y = 4 becomes (6-y)-y = 4. Or 6-2y = 4
Subtract 6 from both sides.
-2y = -2
Divide both sides by -2 and you get y = 1.
Since you know that x = (6-y) you substitute the 1 for y.
x = 6-1 or 5. So x is 5 and y is 1.
For problem 2.
3x + 4y = 20 Subtract 4y
3x = 20 - 4y Divide by 3.
x = (20 - 4y)/3
Plug into equation 2. 3x -2y = 8 becomes
3(20-4y)/3 -2y = 8 or (20-4y) -2y = 8 or 20 - 6y =8
-6y = 8-20 or -12 Divide by -6
y = 2 Since x = (20 -4y)/3 = (20 -8)/3 = 12/3 =4
y is 2 and x is 4.
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1. First equation gives y = 6-x, substitute into second:
x - (6-x) = 4
=> x - 6 + x = 4
=> 2x = 10
=> x = 5
y = 6-x = 1.
So x = 5 and y = 1.
2. Second equation gives 2y = 3x - 8, substitute into first equation:
3x + 2(3x - 8) = 20
=> 3x + 6x - 16 = 20
=> 9x = 36
=> x = 4
2y = 12 - 8 = 4 => y = 2.
So x = 4 and y = 2.
👍 60 | 👎 -13
1) x-y = 4 => x = y+4
sub in y+4 for x in the first equation
(y+4) + y = 6
plug in y = 1 into either equations
x +1 = 6
x = 5
y = 1
2) as you see there is the term "3x" in both equations so solve for that in one of them
3x - 2y = 8 => 3x = 2y + 8
sub in 2y + 8 into the first equation for 3x
(2y + 8) +4y = 20
6y = 12
y = 2
plug y = 2 into either equation
3x + 8 = 20
3x = 12
x = 4
y = 2
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substitute x=5 in any of above equations
therefore solutions are x=5,y=1
sub 2 from 1
substitute y=2 in any of above equations
therefore solutions are x=4,y=2
👍 60 | 👎 -27
Originally Answered: How do I solve this question using the substitution method?
You must have two equations to solve for two unknown variables. The two unknown variables in this case are the number of one bedroom apartments and the number of two bedroom apartments.
One bedroom apartments we'll call "x"
Two bedroom apartments we'll call "y"
Using the word problem we know a few key things:
There are 80 apartments total
The cost of each type of apartment
The total rent
Let's show that we know that the number of apartments is 80:
Mathematically that means when you add the number of one and two bedroom apartments you get the total
We need another equation:
Let's show that we know how to find the total rent using the two types of apartments:
Now we have two equations with x and y in them
To substitute one equation into the other, you must solve one for x or y and put it into the other. The first equation is easier, so as an example let's solve that for x (you could do it for y if you wanted).
Alright, let's plug the value for x into the other equation
Solve for y
Now that you know what y is (number of 2 bedroom apartments) plug it into one of the equations to find x. We'll use the first equation because it is simpler.
solve for x