Question

solve the system with elimination 3x+y=12 and 2x+2y=4

Answer 1

To solve the system using elimination, we want to eliminate one of the variables by manipulating one or both of the equations in some way. Let's start by multiplying the second equation by -1:

-1(2x + 2y) = -1(4)
-2x - 2y = -4

Now, we can add the two equations together:

(3x + y) + (-2x - 2y) = 12 + (-4)
3x - 2x + y - 2y = 12 - 4
x - y = 8

Now we have a new equation: x - y = 8. This equation does not have any coefficients other than 1 for either variable, so we can solve it easily.

x - y = 8
x = y + 8

Now we can substitute this expression for x into either of the original equations. Let's use the first equation:

3x + y = 12
3(y + 8) + y = 12
3y + 24 + y = 12
4y + 24 = 12
4y = 12 - 24
4y = -12
y = -12/4
y = -3

Now that we have the value for y, we can substitute it back into the expression for x:

x = y + 8
x = -3 + 8
x = 5

So, the solution to the system of equations is x = 5 and y = -3.