Solve the system by addition: 3x+2y=13 , x+4y=1?

Question

This is how it would be written:
3x+2y=13
x+4y=1

Answer 1

There are a variety of ways to solve this problem.
This is a system of linear equations. To start with not all systems of linear equations have solutions.
One way to solve this problem is to multiply both sides of the bottom equation by -3
3x+2y=13
-3(x+4y)=-3(1)

Which then becomes:
3x+3y=13
-3x-12y=-3

Adding the top equation to the bottom equation we get:

3x +(-3x) + 3y +(-12y) = 13 + (-3)

Which then becomes (since 3x +(-3x) = 0)
-10y = 10

Divide both sides by -10 to solve for y:

-10y/(-10) = 10/(-10) and we get

y = -1

Since we have found y=-1 as one of our answers, we can now solve for x by substituting in the value of y=-1 into
one of the equations:

Thus for x + 4y=1 and substituting in y=-1 we get:

x +4(-1) = 1
which gives us:

x +(-4) = 1

Add 4 to both sides of this equation:

x + (-4) + 4 = 1 + 4
we get:

x = 5

So our final solution set is:

x=5, y=-1

Answer 2

1 as in, the answer to the question mark is 1 and the final number is 11. Unless I'm reading the question wrong. Which there is a possibility of that.

x=3 and y=2. After the math is done the problem would then read. 9+4=13, 3+8=11

Answer 3

3x+2y=13
x+4y=1

x=-4y+1 Subtraction Prop of Equality
3(-4y+1)=13 substitute
y=-1
x=5

Answer 4

5

Answer 5

you need to subtract one equation from the other. First, you need to make sure that both equations have either the same number of x's or y's to solve for the remaining x or y.
For example, multiply the 2nd equation by 3, so instead of x+4y=1, you have 3x+12y=3. Subtract this from the first equation.
3x+2y=13
-3x+12y=3
=
-10y=10
so y = -1
Now solve for x.
3x+2(-1)=13
3x=15
x=5

Hopefully you are using Yahoo answers not just to get the answer to your homework, but also to learn how to do it.

Answer 6

you can solve it in two different ways:
1. I 3x+2y=13
II x+4y=1
I -6x -4y=-26
I + II -6x-4y+x+4y = -26+1
-5x = -25
x=5 => y=-1

2. I 3x+2y=13
II x+4y=1
II x= 1-4y
I 3(1-4y)+2y = 13
3-12y+2y = 13
-10y = 10
y=-1 => x = 5

(x,y) = (5,1)

Answer 7

By addition x=5 and y= -1

Take x+4y=1 and multiple by negiative three.
Now you have
-3x-12y= -3

Now you can add the two equations and get
-10y=10

y= -1

Now go to x+4y=1 and substitue -1 for y

You now have x-4=1 which means x=5

Answer 8

3x + 2y = 13
x + 4y = 1

(3x + 2y) + (x + 4y) = 13 + 1
3x + 2y + x + 4y = 14
4x + 6y = 14
2x + 3y = 7

3y = -2x + 7
y = (-2/3)x + (7/3)

x + 4y = 1
x + 4((-2/3)x + (7/3)) = 1
x - (8/3)x + (28/3) = 1
3x - 8x + 28 = 3
-5x + 28 = 3
-5x = -25
x = 5

3x + 2y = 13
3(5) + 2y = 13
15 + 2y = 13
2y = -2
y = -1

x = 5
y = -1

Answer 9

3x+2y=13
x+4y=1

Multiply both sides of the first eqaution by 2.

6x+4y=26.
x+4y=1.

Subtract equation two from one.

5x=25

x=5

Substitute 5 for x

5+4y=1

Subtract 5 from each side

4y=-4

y=-1

Now do the rest of your homework yourself.

Answer 10

is this a linear quadratic equation?

if it is then
x=5 & y= -1