Final answer:
To solve the system of equations using elimination method, multiply the equations by constants to eliminate one variable, add them together, solve for the remaining variable, and substitute it back into one of the original equations. The solution to the system is x = -3 and y = 0.
Step-by-step explanation:
To solve the system of equations by elimination method, we need to eliminate one variable by multiplying one or both of the equations by a constant such that the coefficients of the variable will be opposites. Multiplying the first equation by 3 and the second equation by 2 will result in the coefficients of x being opposites. Adding the two equations together will eliminate x. We then solve the resulting equation for y, and substitute the value of y back into either of the original equations to find the value of x.
Multiplying the first equation by 3 gives: -6x + 12y = 18
Multiplying the second equation by 2 gives: 6x + 4y = -18
Adding the two equations together gives: 16y = 0
Dividing by 16, we find y = 0.
Substituting y = 0 back into the first equation gives: -2x + 4(0) = 6, which simplifies to -2x = 6.
Dividing by -2, we find x = -3.
Therefore, the solution to the system of equations is x = -3 and y = 0.
To solve the given system of equations by elimination, we need to eliminate one of the variables. Looking at the coefficients, we see that by multiplying the second equation by 2, it will allow for elimination of 'y'.
Original equations:
-2x + 4y = 6
3x + 2y = -9
Multiplying the second equation by 2:
6x + 4y = -18
Adding the newly formed equation and the original first equation:
-2x + 6x = 6 - 18
4x = -12
x = -3
Substituting 'x' into the first equation:
-2(-3) + 4y = 6
6 + 4y = 6
4y = 0
y = 0
So, the solution to the system of equations is x = -3, y = 0.
Learn more about Solving systems of equations by elimination