Essentially what you would want to do is eliminate a variable so you have to multiply the two equations so that the two “y”s cancel each other out. You do this by multiplying one by a negative number and the other one a positive number. Doesn’t matter what number you multiply the number with; however, both numbers need to be the same distance away from zero. Also, if you’re going to multiply one term, then all the terms will need to be multiplied.
-5(5x+3y)=-10 3(3x+5y)=-6
Distribute and Multiply: -25x-15y=50 9x+15y=-18
Now add the two equations by adding the x’s together, y’s, and the total.
The y’s end up canceling each other.
-16x=32
Divide:
X=-2
Now that you have “X” substitute x from one of the equations from the beginning. You may do two for checking answers.
C = 180 - (22 + 105) = 180 - 127 = 53 degrees Area of triangle = 1/2 ab sin C But a / sin A = b / sin B or a = b sin A / sin B = (14 x sin 22) / sin 105 = 5.429 Therefore, Area of triangle = 1/2 x 5.429 x 14 x sin 53 = 30.4 units^2
