Solve using linear combination

Question

4x-3y=10

5x+6y=-7

(Same question)

Answer 1

Here's the procedure to solve a system of equations using Linear Combination:

1. Rearrange the equations so terms line up as: Ax + By = C
2. Multiply none, or one, or both equations by constant(s) so that the coefficients of one of the variables are opposites.
3. Add the two equations together to eliminate one of the variables.
4. Solve.
5. Use one of the equations and this value to solve for the other variable.

 

4x - 3y = 10

5x + 6y = -7

1. These equations are already in the form Ax + By = C, so we don't need to do any rearranging
2. Let's multiply the first equation by 2 to turn the -3y term into a -6y term to cancel the +6y term in the second equation

 

2*(4x - 3y) = 2*10

8x - 6y = 20

 

    3.  Now let's add this equation to the 5x + 6y = -7 equation

 

8x - 6y+ 5x +6y = 20 - 7  (the -6y cancels the +6y)

13x =  13

 

    4. Solve for x. 

 

    5.  Plug the value of x you get back into one of the original equations to solve for y.