Question

Solve using elimination

3x + y = 10 - 2x + 2y = 12

Answer 1

To solve using elimination, we first need to make sure that one of the variables has the same coefficient for both equations. In this case, it is easier to make the coefficients of x equal in both equations.

Given equations:
1) 3x + y = 10
2) -2x + 2y = 12

To make the coefficients of x equal, we can multiply the first equation by 2 and the second equation by 3:

1) 6x + 2y = 20
2) -6x + 6y = 36

Now, subtract the second equation from the first:

6x + 2y - (-6x + 6y) = 20 - 36
6x + 2y + 6x - 6y = -16
12x - 4y = -16

Now divide the entire equation by 4 to simplify:

3x - y = -4

Now we have a simpler equation:
3x - y = -4
y = 3x + 4

Now we can substitute y = 3x + 4 into either of the original equations to solve for x:

3x + (3x + 4) = 10
6x + 4 = 10
6x = 6
x = 1

Now that we have the value of x, we can substitute it back into y = 3x + 4 to solve for y:

y = 3(1) + 4
y = 3 + 4
y = 7

Therefore, the solution to the system of equations is x = 1 and y = 7.