Question

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

Answer 1

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.