Math Problem 5?

Question

Solve the system:

x - 3y = 5

4x + y = 7

Answer 1

x - 3y = 5- - - - - -Equation 1
4x + y = 7- - - - - Equation 2
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Substitute method equation 2

4x + y = 7

4x + y - 4x = 7 - 4x

y = 7 - 4x

The answer is y = 7 - 4x

Insert the y value into equation 1

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x - 3y = 5

x - 3(7 - 4x) = 5

x - 21 + 12x = 5

13x - 21 = 5

13x - 21 + 21 = 5 + 21

13x = 26

13x / 13 = 26 / 13

x = 2

The answer is x = 2

Insert the x value into equation 1

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x - 3y = 5

2 - 3y = 5

2 - 3y - 2 = 5 - 2

- 3y = 3

- 3y/- 3 = 3 / - 3

y= - 1

The answer is y = - 1

Insert the y = - 1

Insert the y value into eqution 1

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Check for equation 1

x - 3y = 5

2 - 3(- 1) = 5

2 - (- 3 = 5

2 + 3 = 5

5 = 5

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Check for equation 2

4x + y = 7

4(2) + ( - 1) = 7

8 - 1 = 7

7 = 7

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The solution set is { 2, - 1 }

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Answer 2

You can either solve this by elimination or by substitution. I'll show you both methods:

Elimination:

The gist of elimination is to multiply an equation by a certain value, and then subtract (or add) the two equations together such that it eliminates one of the variables. So we have

x - 3y = 5
4x + y = 7

Let's multiply the first equation by 4.

4x - 12y = 20
4x + y = 7

Now, let's subtract those equations. This will result in (4x - 4x), which is obviously 0. We would also be left with

-12y - y = 20 - 7, which we can solve algebraically.
-13y = 13, or
y = -1.

Now, all we have to do is plug this into any one of the two equations and we'll get x. Let's choose the first equation.

x - 3(-1) = 5, or
x + 3 = 5, or
x = 2

Therefore, the solution is x = 2, y = -1.

Second method: Solving by substitution.

When solving by substitution, we solve for one variable in one equation, and then plug this into the other equation.

x - 3y = 5
4x + y = 7

Let's solve for x in the first equation.
x - 3y = 5, Bringing the -3y over to the right hand side yields
x = 3y + 5

Now, we take the second equation 4x + y = 7, and substitute what we just worked x out to be.

4[3y + 5] + y = 7. Expanding, gives us
12y + 20 + y = 7
13y = -13
y = -1

Now, we just substitute this into any one of the two equations. During the method of elimination, we chose the first equation to plug y = -1 into; let's choose the 2nd one this time, to show you that it doesn't matter.

What we're choosing is 4x + y = 7. Plugging in y = -1, we get
4x + (-1) = 7
4x = 8
x = 2

Therefore, x = 2 and y = -1.

Which method is better? It depends. Sometimes, you'll get a system of equations like:

4x + 2y = 7
8x + 9y = 3

where it is obvious that elimination is better; in this case, we can clearly see that 8 is a multiple of 4.

In cases like this:

x + 8y = 0
9x + 44y = 88

Notice that x is by itself for the first equation. This might be best solved by substitution, since solving for x is a one-step process.

Those are your weapons of choice: elimination and substitution.

Answer 3

First you make (x) alone by adding 3y to both side:
x=3y+5
Then you substitute the solution to x into 4x+y=7
4(3y+5)+y=7
Then you solve it:
4x3y=12y
4x5=20
12y+20+y=7
13y+20=7 7-20= -13
13y= -13
y= -1
Finally you substitute the answer to y which is -1 to either one of the problem:
x - 3(-1) = 5
x+3=5
x =2
or
4x + y =7
4x + (-1) = 7
4x-1=7
4x = 8
x= 2

Answer 4

2 equations 2 unknowns.
isolate the same value for each set them equal and solve for the other value sub back in to one equation and solve for the other

isolate x in each
1)
x=5+3y
2)
x=(7-y)/4

set them equal
1)=2)
5+3y=(7-y)/4

solve for y
4(5+3y) =7-y
20+12y =7-y
20-7=-y-12y
13=-13y
13/-13=y
y=-1

sub found y value into one of the equations lets do 1)
x=5+3(-1)
x=5-3
x=2
therefor in the system intersects at (2,-1).

you can do a check by subbing in x and y to the original equations

Answer 5

The first gives x =5+3y

and 20+12y +y =7

13y =-13
y = -1 and x=2

Answer 6

x - 3y = 5
4x + y = 7

x-3y=5
12x+3y= 21

13x=26
x= 2

2-3y=5
-3y=3
y= -1

(2,-1)

Answer 7

12x+3y=27
(multilplying by 3)
x-3y=5
y is eliminated
13x=32
x=32/13

y becomes 32/13-3y=5 and you can finsih the rest .ove you

Answer 8

x-3y=5..................(1)
4x+y=7...................(2) multiplying by 3

x-3y=5
12x+3y=21 by adding the two new equation we get
13x=26 then x=2
In equation (2)
4(2)+y=7
8+y=7 y=7-8=-1
THEN x=2 ,y=-1

Answer 9

x=2
and
y= -1