Question

How do you solve the system `4x-y=25` and `4x+5y=-29`?

Answer 1

use the elimination method to solve the simultaneous equations:
4x-y=25>eq no 1
4x+5y=-29>eq no 2
eq no 1-eq no 2
4x -y =25
(-4x-5y=29)the signs become opposite in the subtraction
0 -6y =54
-6y=54
y=54/-6
y=-9.

put the value of y=-9 into eq no 1.
(try to put the value in the equation with smaller values)
4x-(-9)=25
4x+9=25
4x=25-9
4x=16
x=16/4
x=4
S.S{4,-9}(remember that the value of the variable which comes first according to the alphabetic arrangement is always written first)

Answer 2

`{x,y}={-9,4}`

Explanation:

Solve by elimination and substitution

`color(blue)(4x-y=25`

`color(blue)(4x+5y=-29`

We could see that, we can eliminate `4x` from both the equation

Subtract

`rarr(4x-y=25)-(4x+5y=-29)`

`rarr-6y=54`

`color(green)(rArry=54/-6=-9`

Substitute the value of `y` to the first equation

`rarr4x-(-9)=25`

`rarr4x+9=25`

`rarr4x=25-9`

`rarr4x=16`

`color(green)(rArrx=16/4=4`

`:.color(purple)({x,y}={-9,4}`