(substittion method) x-y=2&4x-3y=11 next problem -2x+3y=14&x+2y=7?

Answer 1

first problem

x-y = 2
4x - 3y= 11

use first equation to find out what x or y is (relative to other variable)

x=2+y
or
y=-2 + x

put the value for x or y into the second equation and use algebra to find the value of one of the variables.

4(2+y) - 3y= 11
8 + 4y - 3y =11
y=3

put the value of y into an equation and solve for x.
x-(3)=2
x=5

First problem: x=5, y=3.
check answers:

4(5)-3(3)=11 ---- yes, the values are correct.


Second problem:

-2x+3y=14
x+2y=7

use the second equation to find out what x is
x=7-2y

put value into first equation, use algebra to find y
-2(7-2y)+ 3y=14
-14+4y + 3y=14
7y=28
y=4

substitue 4 as the value of y in an equation
x+2(4)=7
x=-1

In this problem, x=-1 and y=4.

check answers:
(-1)+ 2(4)=7 :) answers are right

hope this helped

Answer 2

Problem 1: x = 5, y = 3

x - y = 2
4x - 3y = 11

x - y = 2      >>>      x = 2 + y
4x - 3y = 11      >>>      4 ( 2 + y ) - 3y = 11
8 + 4y - 3y = 11
8 + y = 11
y = 3
x = 2 + ( 3 )
x = 5

Problem 2: x = -1, y = 4

-2x + 3y = 14
x + 2y = 7

x + 2y = 7      >>>      x = 7 - 2y
-2x + 3y = 14      >>>      -2 ( 7 - 2y ) + 3y = 14
-14 + 4y + 3y = 14
-14 + 7y = 14
7y = 28
y = 4
x = 7 - 2 ( 4 )
x = 7 - 8
x = -1

Answer 3

The substitution method is a way of solving a "system of equations". A system of equations is just two or more equations that you are trying to solve together.

What you are trying to do is find the point where these two linear equations intersect. So you need the point (x,y) that works in BOTH equations. There are several ways to find this answer.

So now to the substitution method. In this method of solving you take ONE of the equations and solve it for one of the variables. For the two equations you've written: x - y = 2 and 4x - 3y = 11, the first equation will be easiest to solve for a variable since there isn't a coefficient on either of the variables. So:

x - y = 2
+y +y add y to both sides to remove it from the left side

x = y + 2

Now you have this "value" of what x must equal (y + 2). We now take that value and substitute it into the other equation wherever you have an x.

4x - 3y = 11
4(y + 2) - 3y = 11 substitute what x equals
4y + 8 - 3y = 11 distribute
y + 8 = 11 combine like terms
-8 -8 subtract 8 to remove it from left side
y = 3 simplify

So NOW we now what y equals

Now that we have a value for y, we will plug it back into the equation we solved for x.

x = y + 2
x = 3 + 2
x=5

Now we have both the x and y value of the point where the equations intersect, and this is our solution to the system.

(x, y) = (5, 3)

On to your second system of equations.

-2x + 3y = 14
x + 2y = 7

The x in the second equation will be the easiest to get by itself.

x + 2y = 7
-2y -2y add opposite to remove the y term from left side

x = -2y + 7

Now substitute that value for x into the first equation.

-2x + 3y = 14
-2(-2y + 7) + 3y = 14 substitute
4y - 14 + 3y = 14 distribute
7y -14 = 14 combine like terms
+14 + 14 add opposite of constant term
7y = 28 simplify
(1/7)7y = (1/7)28 multiply by reciprocal of coefficient on y
1y = 4

Now we now the value of y, and we substitute that back into the equation we solved for x.

x = -2y + 7
x = -2(4) + 7 substitute
x = -8 + 7 multiply
x = -1 simplify

So we now know the x and y values of our solution, and we write the answer as the coordinate point (-1, 4).

In both of your examples it was easiest to solve one of the equations for an x term. But that isn't always the case. Remember, you are looking for the one variable between the two equations that doesn't have a coefficient in front of it.

Good luck! I hope this helps.

Answer 4

1. y=x-2
4x-3(x-2)=11
4x-3x=11-6
x=5
y=5-2
y=3

2. x=7-2y
-2(7-2y)+3y=14
4y+3y=14+14
7y=28
y=4
x=7-2(4)
x=-1

Answer 5

You have to get one variable by itself. So for the first problem it would be y=2-x, then 4x-3(2-x)=11. The next problem would be X=7-2y, then -2(7-2y)+3y=14. Hope this helped.

Answer 6

problem 1
x-y=2
or x=2+y
put this value in 2nd equation
4x-3y=11
or 4(2+y)-3y=11
or 8+4y-3y=11
or 8+y=8+3
so y=3
and x=y+2=3+2=5
so x=5, y=3 is the answer of first question

problem 2
x+2y=7
so x=7-2y
putting this value in 2nd equation we get
-2x+3y=14
or -2(7-2y)+3y=14
or -14+4Y+3y=14
or 7y=28
or y=4
from 1st equation we have
x=7-2y
putting value of y in this we get
x=7-8=-1
so answer of thsi problem is x= -1, y=4

Answer 7

1)
x-y=2 so x=2+y
4(2+y)-3y=11
8+4y-3y=11
8+y=11
y=3
x-3=2 so x=5

2)
x=7-2y
-2(7-2y)+3y=14
-14+4y+3y=14
7y=28
y=4
x=7-2(4) so x=-1

Answer 8

x-y=2
4x-3y=11
solve x=y+2
Sub
4(y+2)-3y=11
4y+8-3y=11
8+y=11
y=3
~~~~~~~~~~~~~~
2x+3y=14
x+2y=7
solve x=7-2y
2(7-2y)+3y=14
14-4y+3y=14
14-y=14
y=0

Answer 9

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