Solve using linear combination. 8x+14y=4 - 6x-7y+-10

It's best to write the two equations as a vertical column:

8x+14y=4

-6x-7y = - 10

Note that if we multiply the 2nd equation by 2, we get - 12x - 14y = - 20. The reason for wanting this version of the 2nd equation is that its - 14y cancels the + 14y in the first equation:

-12x - 14y = - 20

8x+14y=4

Combine these equations, column by column. We get - 4x = - 16, which results in x = 4. Now find y by subbing 4 for x in either given equation. If we use the first equation, we get 8 (4) + 14y = 4, or 32 + 14y = 4, or 14y = - 28. Then y = - 2.

The solution to this system of linear equations is thus (4,-2).

Check this result by substitution of these coordinates into - 6 (4) - 7y = - 20:

-24 - 7 (-2) = - 10. Is this true or not?

-24 + 14 = - 10 is true. Thus, (4,-2) is the desired solution.