Solve by the elimination method.
2x-7y=-36
7x+2y=33
2x-7y = -36,so
2x = 7y-36
x = (7y-36)/2
plug that into the other equation:
7*(7y-36)/2 + 2y = 33
49y - 258 + 4y = 66
y = 6
so, x = 3
To solve the system of equations using the elimination method, we must eliminate one variable by adding or subtracting the two equations. In this case, let's eliminate the x variable.
Step 1: Multiply one or both equations by an appropriate number so that the coefficients of x in both equations are opposites. Looking at the coefficients of x in both equations (2x and 7x), we can multiply the first equation by 7 and the second equation by 2, resulting in:
1) 14x - 49y = -252
2) 14x + 4y = 66
Step 2: Subtract equation 2 from equation 1 to eliminate x. This will give us an equation in terms of y only.
(14x - 49y) - (14x + 4y) = -252 - 66
14x - 14x - 49y - 4y = -318
-53y = -318
Divide both sides of the equation by -53:
y = -318 / -53
y = 6
Step 3: Substitute the value of y back into one of the original equations to determine the value of x. Let's use the first equation:
2x - 7(6) = -36
2x - 42 = -36
2x = -36 + 42
2x = 6
Divide both sides of the equation by 2:
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 6.