Maths help! Simultaneous Equations?

Question

Could you help me figuer out the value of x and y if..

3x + 5y = 11
2x + y = 3

And could you show me the workings out please so I can learn to do the method. Thanks.

x

Thanks for all the help! x

Answer 1

first u have to multiply or divide one of the equations, so that one of the variables cancels out

for example
in the 1st eqn u have "5y"
in the 2nd eqn u have "y"

so if u multiplied the 2nd equation by "5" everywhere, then the y's would cancel

so now u have

3x + 5y = 11
and
5*2x + 5*y = 5*3
or

3x + 5y = 11
10x + 5y = 15

the next step is to subtract the new 2nd eqn. from the first

so youre left with

-7x = -4
solve for x
x = 4/7

now plug this value of x into any one of the original equations (ill choose the original 2nd eqn because it's easier)

2(4/7) + y = 3 and solve for y

8/7 + y = 3
8/7 + y = 21/7
y = 13/7

so x = 4/7 and y = 13/7 is your answer

Answer 2

there are many methods to solve simultaneous equations - the main ones being by elimination, by direct substitution, the matrix method, and the graphical method.

probably the easiest method for small examples like this is the substitution method.

the idea is to take one of the equations and get one of the variables 'in terms' of the other variable, and then to substitute that into the other equation so that only one variable remains. that equation may then be solved directly as its in a single variable, and from that the other variable can be found easily.

the first thing to do however is label your equations, lets call them 1) and 2), so :-

3x + 5y = 11 (1)
2x + y = 3 (2)

now, looking at equation (2) we can see it contains a single 'y', so lets choose this variable to be the one we isolate (ie. get on its own on the left hand side), so if we treat equation (2) like any other equation and use the 'change the side change the sign' rule, then equation (2) becomes :-

y = 3 - 2x (2)

now if we use this expression for 'y' and substitute it into equation (1), then we get :-

3x + 5(3 - 2x) = 11
so, 3x + 15 - 10x = 11
-7x = 11 - 15 = -4
so, x = 4/7

now using this value of 'x', we can find our 'y' from y = 3 - 2x,
so, y = 3 - 2(4/7) = 3 - 8/7 = 13/7 = 1 6/7

x = 2 2/7 and y = 1 6/7

Answer 3

I start out differently. I'd take the 2nd equation and rearrange it to solve for y. Subtract 2x from both sides:

2x + y - 2x = 3 - 2x

*y = 3 - 2x we'll get back to this later.

Now literally stack both equations on top of each other

3x + 5y = 11
2x + 1y = 3

Now we're going to 'combine' the two equations to solve for 1 variable. So choose a variable to 'eliminate'. I choose y because it's simpler and I already know the answer, but you can choose x if you want to. You'll see in a sec...

Multiply the bottom equation so that the coefficient of the variable you want to eliminate matches the coefficient of the same variable of the top equation. Here we multiply by 5.

3x + 5y = 11
5 x (2x + y = 3)

3x + 5y = 11
10x + 5y = 15

Subtract the lower equation from the top.

3x + 5y = 11
-10x - 5y = -15
____________
-7x + 0y = -4

so now we have:

-7x = -4 (divide by -1)
7x = 4 (divide by 7)
x = 4/7

Remember when we solved for y earlier?

*y = 3 -2x so

y = 3 - 2(4/7)

y = 3 - 8/7

y = 3(7/7) - 8/7

y = 21/7 - 8/7

y = 13/7, x = 4/7

Answer 4

First isolate y in the second equation
2x + y = 3
y = 3 - 2x

Now substitute this y value into the first equation
3x + 5y = 11
3x + 5(3 - 2x) = 11

Solve for x
3x + 5(3 - 2x) = 11
3x + 15 - 10x = 11
3x - 10x = 11-15
-7x = -4
x = 4/7

Now substitute this value of x into the second equation
2x + y = 3
2(4/7) + y = 3

Solve for y
y = 3 - 2(4/7)
y = 13/7

Hope this helps :)

Answer 5

3x + 5y = 11
2x + y = 3

Muliply the second equation with 5
5*(2x+y=3)
10x+5y=15

now subract this from equation 1
3x + 5y = 11
10x+5y=15
-----------------------------
-7x+0y=-4
-7x=-4
7x=4
x=4/7
so

substitute this vakue of x in equation2
2x+y=3
2(4/7)+y=3
8/7+y=3
y=3-8/7
take lcm
y=(21-8)/7
y=13/7

check
substitute these values of x & y in equation 1
3x+5y=11

in the left hand side
3(4/7)+5(13/7)
12/7+65/7
(12+65)/7
77/7
11
this is the answer on the right so the values of x & y are correct

Answer 6

multiply second eqn. by -5
now you have
3x + 5y = 11
-10x - 5y = -15
add these to eliminate the y terms
-7x = -4 so x = 4/7

take 2x + y = 3 and substitute for x
2(4/7) + y = 3
y = 3 - 8/7 == 21/7 - 8/7 == 13/7

(4/7 , 13/7) is the answer

~~

Answer 7

NUMBER EQUATIONS: 3x+5y=11 (1)
2x+y=3 (2)

MULTIPLY (2) BY 5 10x+5y=15 (3)

SUBTRACT(1) FROM (3) 7x=4
x=4/7

SUB VALUE FOR X INTO (2) 2x+y=3
8/7+y=3
y=2 and 5/8

HOPES THIS HELPS...:)

Answer 8

hi
i used to be rubbish at these but this year it has clicked
(a)3x + 5y = 11 (x2)
(b)2x + y = 3 (x3)
get one of the letters the same on ecah equation
=
(a)6x+ 10y= 22 and(b) 6x+3y = 9
take b away from a you get
7y= 23
so y = 13/7
substitue 13/7 into one equation you get
2x+ 13/7=3
2x=3- 13/7
2x=1.1492 to 4d.p
x=0.5714

hope it helps

Answer 9

3x + 5y = 11
- 10x - 5y = - 15 -----ADD
- 7x = - 4
7x = 4
x = 4 / 7

8/7 + y = 3
y = 21/7 - 8/7
y = 13 / 7

x = 4 / 7 , y = 13 / 7

Answer 10

3x + 5y = 11
-5(2x + y = 3)

3x + 5y = 11
-10x-5y =-15

-7x=-4
x=4/7

3(4/7)+5y=11
12/7+5y=77/7
5y=65/7
y=(65/7)(1/5)=65/35=13/7

ANSWER
(4/7, 13/7)