Solving Simultaneous Equations: 3x + y = 17 and 4x - 2y = 6

[hannahbanana99]

hi i am stuck on these simulateous equations -

4x - 2y = 6
3x + y = 17


and this one

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

please please help me
thanks

 

[arildno]

What have you done so far?

 

[Trail_Builder]

do you know the basics of simuelteanous equations? (ie how to eliminate one of the values, or substiting one into the other?)

 

[pugfug90]

"4x - 2y = 6
3x + y = 17"

Take one of those equations, isolate one of the variables, then plug it into the other equation. That will figure out one variable, and with that one variable, you can plug into either original formulas to get the other variable.

Example, change the 2nd to y=17-3x. Plug that y into 4x-2y=6.. that should be 4x-2(17-3x)=6..and follow the rest of my instructions.

 

[Alex13]

The other method you can use is elimination, meaning adding or subtracting the equations.


multiply one of the equations (sometimes it isn't necessary)

7a - 3b = 17
3(2a + b = 16)

if you multiply this equation by 3, you will have "3b" in both equations.



now you can subtract or add the equations together to eliminate one of the variables

7a - 3b = 17
+(6a + 3b = 48)

so, 13a = 65


you can take it from here. once you figure out one variable, you can figure out the other with simple algebra

Alex