Answer and Step-by-step explanation:
Given the system of equations:
2x – 5y = 13
–3x + 2y = 13
We can decide to eliminate either x or y in order to solve the simultaneous equations.
1. To eliminate x:
Multiply the first equation by the coefficient of x in the second equation and multiply the second equation by the coefficient of x in the first equation. By doing this the coefficients of x in the equations would be the same and subtracting them to be equal to zero becomes easy, thus eliminating that variable.
The coefficient of x in the second equation is –3, if we multiply the first equation by it we have:
–6x+15y = –39
The coefficient of x in the first equation is 2, if we multiply the second equation by it we have:
–6x+4y = 26
Subtracting the resulting equations we have:
11y = –65 and x is eliminated.
2. To eliminate y:
Multiply the first equation by the coefficient of y in the second equation and multiply the second equation by the coefficient of y in the first equation. By doing this the coefficients of y in the equations would be the same and subtracting them to be equal to zero becomes easy, thus eliminating that variable.
The coefficient of y in the second equation is 2, if we multiply the first equation by it we have:
4x–10y = 26
The coefficient of y in the first equation is –5, if we multiply the second equation by it we have:
15x–10y = –65
Subtracting the resulting equations we have:
–11x = 91 and y is eliminated.
