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

Sep 16, 2016

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)

Sep 16, 2016

$\left\{x , y\right\} = \left\{- 9 , 4\right\}$

#### Explanation:

Solve by elimination and substitution

color(blue)(4x-y=25

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

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

Subtract

$\rightarrow \left(4 x - y = 25\right) - \left(4 x + 5 y = - 29\right)$

$\rightarrow - 6 y = 54$

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

Substitute the value of $y$ to the first equation

$\rightarrow 4 x - \left(- 9\right) = 25$

$\rightarrow 4 x + 9 = 25$

$\rightarrow 4 x = 25 - 9$

$\rightarrow 4 x = 16$

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

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