SOLUTION: I need to solve each system by the addition method, I understood the first problem and got it right but for some reason I am drawing a blank on this one..can someone help? {{{3x

Algebra ->  Linear-equations -> SOLUTION: I need to solve each system by the addition method, I understood the first problem and got it right but for some reason I am drawing a blank on this one..can someone help? {{{3x      Log On


   

Question 124552: I need to solve each system by the addition method, I understood the first problem and got it right but for some reason I am drawing a blank on this one..can someone help?
3x+%2B+4y+=+-5
5x+%2B+6y+=+-7
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The key here is to adjust one or both of the equations so that you have the same number of variables (x or y) in both equations before adding/subtracting.
This way, you eliminate one of the variables leaving you with one equation with one unknown.
1) 3x%2B4y+=+-5 Multiply this equation by -3.
2) 5x%2B6y+=+-7 Multiply this equation by 2.
1a) -9x-12y+=+15
2a) 10x%2B12y+=+-14 Now we can add the two equations to eliminate the y.
3) x+=+1 Now substitute this value of x into either one of the original equations to solve for y.
1)3x%2B4y+=+-5 Substitute x = 1
3%281%29%2B4y+=+-5 Subtract 3 from both sides.
4y+=+-8 Divide both sides by 4.
y+=+-2
The solution is (1, -2)
To check this solution, we can graph the two lines represented by these equations and see if they intersect at the point (1, -2)
graph%28600%2C400%2C-2%2C2%2C-3%2C1%2C%28-3%2F4%29x-5%2F4%2C%28-5%2F6%29x-7%2F6%29