Question

Solve the following system of equations by the elimination method:

18x + 23y = –5, 23x + 18y = 5

Answer 1

Given the system of equations:

18x + 23y = –5   ...(1)

23x + 18y = 5   ...(2)

Step 1: Multiply the equations to align coefficients for elimination

To eliminate (y), multiply equation (1) by 18 and equation (2) by 23 to make the coefficients of (y) the same numerically:

18 × (18⁢x + 23y) = 18 × (–5)

23 × (23x + 18⁢y) = 23 × 5

Which gives: 

324x + 414⁢y = –90 

529⁢x + 414⁢y = 115

Step 2: Subtract the two equations to eliminate (y)

(324x + 414y) – (529x + 414y) = −90 – 115 

324x − 529x + 414y – 414y = –205 

–205x = –205 

`x = (-205)/(-205)`

x = 1

Step 3: Substitute (x = 1) into one of the original equations to find (y)

Using equation (1):

18(1) + 23y = –5

18 + 23y = –5

23y = –5 – 18

23y = –23

`y = (-23)/23`

y = –1

The solution to the system is x = 1, y = –1.