Linear Combination
Rules:
Multiply 1 or both equations by a constant number to obtain coefficients.
Add revised equations (like terms).
there are 13 lighthouses, 2 of them work per every 3 years and there are also 4 of them that work every 2 years.
there are 8 lighthouses, 4 of them work per every 1 year and there are also 5 of them that work every 2 years.
find the values of x and y for the lighthouses.
2x-4y=13
4x-5y=8
1. take the 2x-4y=13 and multiply by -2. creating -4x+8y=-26. by doing this you can cancel out your x values.
2. since your x values are killed off now you should have 12 equations like this, 8y=-26 and -3y=8.
3. now solve for y, add both equations together giving you 3y=-18, now solve and you get y=-6.
4. now go back to the problem that was multiplied earlier by -2 and put y in. the problem should look like 2x-4(-6)=13. solve for x, 2x+24=13, subtract 24 from both sides, giving you 2x=-11, and x=-11/2.
therefore your values are (-11/2,-6)