more math help??

Question

5x-y=10
7x-2y=11
please help...its algebra...duh...but i have many problems like this and i dont get it

Answer 1

im assuming this is a system of equations

so, double the first equation

10x - 2y = 20
7x - 2y = 11

subtract the two equations

3x = 9
x = 3

plug that back in to one of the equations

5(3) - y = 10
15 - y = 10
y = 5

Answer 2

You have 2 equation in 2 unknowns (x and y)
You can solve for one of the unknowns by eliminating the other unknown like this-

Multiply (5x-y=10) by -2
-10x +2y = -20

Now add (7x - 2y = 11) to the result-

-10x + 2y= -20
7x - 2y = 11

-3x + 0y = -9 the result of the addition
3x = 9 so x = 3

Now substitute 3 for the value of x in either equation to solve for y
7 times 3 - 2y =11
21 - 2y =11
10 = 2y so y = 5

First look for the variable that is easier to eliminate by addition or subtraction. Since the 1st equation has -1y as a term and the 2nd equation has -2y as a term, if you can modify the first equation so that it has a +2y term, adding the equations together will cause the y term to go to zero.

Answer 3

Rearranging the 1st equation:

5x-y = 10 becomes y = 5x-10

You then replace y in the 2nd equation with 5x-10:

7x-2y = 11 becomes 7x-2(5x-10) = 11

or 7x - 10x + 20 = 11 (remember that -2 times -10 = +20)
or -3x + 20 = 11

add 3x to both sides to get:

20 = 11 + 3x

subtract 11 from both sides to get

9 = 3x

so x = 3. since y = 5x-10 we know that y = 15-10 = 5

We can check this:

5(3) - 5 = 15 - 5 = 10
7(3) - 2(5) = 21 - 10 = 11

Answer 4

Use substitution...

5x-10=y which makes the second problem

7x-2(5x-10)=11

you should get it from there

edit: 7x-10x+20=11
-3x=-9
x=3

check with the equation
5(3)-y=10 y=5
7(3)-2(5)=11

answer is x=3 and y= 5 or (x,y) so (3,5)

hope this helped

Answer 5

Isolate "x" or "y" in either equation. Let's solve for "x" in the 1st eqution.

First: add "y" to both sides (when you move a term to the opposite side, always use the opposite sign).

5x - y +y = 10+y
5x = 10+y (Divide each term by 5).
5x/5 = 10/5+y/5
x = 2+y/5

SEc: substitute 2+y/5 with "x" in the 2nd equation.

7(2+y/5) - 2y = 11
14+7y/5 - 2y = 11
14 - 3y/5 = 11 (subtract 14 from both sides).
14-14 - 3y/5 = 11-14
- 3y/5 = -3 (multiply both sides by -5/3)
(- 3y/5)(-5/3) = (-5/3)(-3)
y = 15/3
y = 5

Third: replace/substitute 5 with "y" in the 1st equation.

5x - 5 = 10 (add 15 with both sides).
5x - 5+5 = 10+5
5x = 15 (divide both sides by 5).
5x/5 = 15/5
x = 3

Solution Set: (3, 5)

Answer 6

in this problem, you need to solve for either x or y in one of the equations then plug into the other one. lets solve for y in the first equation (i think that is the easier one)

5x-y=10 subtract 5x from both sides
5x-y-5x=10-5x
-y=10-5x now, multiply each side by -1
-1(-y)=-1(10-5x)
y=-10-(-5x)
y=-10+5x = 5x-10

take the solution for y and plug that into the second equation

7x-2y=11
7x-2(5x-10)=11
7x-(10x-20)=11
7x-10x+20=11 combine like terms and subtract 20 from each side
-3x+20-20=11-20
-3x=-9 divide -3 on each side
x=3 plug that into our equation for y

y=5x-10
y=5(3)-10=15-10=5

now, lets check our work...in the first equation
5(3)-5=10 ?
15-5=10
10=10 good!

second equation
7(3)-2(5)=11 ?
21-10=11
11=11 good!

Answer 7

You need to add the two equations together to eliminate one of the variables. Multiply the first equation by -2

5X-y=10 times -2 is the same as
-10x+2y=-20 (now add these two equations together)
7x-2y=11
equals
-3x=-9
x=3

plug 3 back into either equation.
5(3)-y=10
15-y=10
-y=-5
y=5

If you plug both varibles into the second equation it should work.

Kind of tought to explain. Good luck.