simultaneous equations?

Question

i cant do these equations please help me !
1st one -
4x - 2y = 6
3x + y = 17

2nd one -
7a - 3b = 17
2a + b = 16

please help !
thanks
hannah

Answer 1

First one - x= 4, y=5
Change the second equation to 6x + 2y = 34
Add the equations, you get 10x = 40; x=4

Second one - a=5, b=6
Change the second equation to 6a + 3b = 48
Add the equations, you get 13a = 65; a=5

Answer 2

Hannah

In general I avoid things that look like 'do my work'...but let's talk over these.

The technique for solving a system of simultaneous equations is to resolve one variable in terms of the other. It can only work if you have as many equations as you have variables.

Your first one
4x - 2y = 6
3x + y = 17

Looking at the two equations, pick one to re-write...the second looks inviting

3x + 7 = 17
let's subtract 3x from both sides...as long as you do the same thing to both sides the equality remains true...
3x + y = 17
- 3x = - 3x
--------------------------
y = 17 - 3x

Now let's use that in the first equation...

4x - 2(17-3x) = 6

4x + (-2)(-3)x + (-2)(17) = 6
or
4x + 6x -34 = 6
or
10x - 34 = 6
again...same thing to both sides...

10x - 34 = 6
+ 34 = + 34
-----------------------
10x = 40

now divide both sides by 10 and you get x=4

we know that y = 17 - 3x so

y = 17 - 3 (4)
y = 5

So...now that I did one...you try the other again and see what you find. Follow the same technique. Solve for b in terms of a using one of the equations. Then substitute that 'value' into the
other equation to solve for the now single variable.

Answer 3

4x - 2y = 6
3x + y = 17
multiply second by 2
6x + 2y = 34
add first to second so y is eliminated
10x = 40
so x = 4
backsubstitute
16 - 2y = 6
so 2y = 10
so y = 5

so if you can use similar process on second, then you wont be afraid of these

Answer 4

1. 4x - 2y=6.............(i)
3x+y=17................(ii)
multiplying (i) with 3 and (ii) with 4
12x-6y=18........(iii)
12x+4y=68.........(iv)
subtracting iii and iv
-10y=-50
y=5
putting the value of y in ii
3x+y=17
3x+5=17
3x=12
x=4

2.7a-3b=17...........i
2a+b=16......ii
multiplying ii with 3..
6a+3b=48..............iii
adding i and iii
13a=65
a=5
putting the value of a in ii
2a+b=16
10+b=16
b=6..
done!!!