Solve the system of equations: 2x+y=5 2x-4y=0
The method I will use here is the addition method (or Combination method). The goal is to add the two equations together in such a way that one variable or another is canceled out. First lets subtract the second equation from the first: 2x + y = 5 -2x +4y = -0 (notice the signs are all opposite of what they were to start with) added together these give us 5y=5. Then divide by 5 we find that y=1 Now lets reset and find out what x equals. If we multiply the first equation by 4 we get: 8x + 4y = 20 (why did we do this? Observe the second equation copied on the next line:) 2x - 4y = 0 (notice that the y's will not cancel each other out - this is why we multiplied by 4) Add these two equations and we get 10x=20; divide by 10 and we find that x=2. The final answer to the solution can be written: x=2, y=1 but is more commonly written as the ordered pair: (2, 1)
What is the exact sine of 30 degrees?
The easiest way to find the sine of an angle is to find a right triangle that has that angle in it. Then you use the old Soh-Cah-Toa rule: Sine = the side opposite the angle / the Hypotenuse. In this case we do have such a triangle, our old friend the special 30-60-90 triangle. Remember that the short side (always across from the 30 degree angle) is always half of the long side (which is always the hypetenuse - across from the right angle). Now if you take a number and divide it by another number that is twice as big the ratio is alway one half. So the sine of 30 degrees is one half.
What is the slope of the line described by the equation: 3x+2y=8?
The best way to find the slope of a line from an equation is to transform the equation into Slope-Intercept form. Essentially we want to make the equation tell us what y equals. So first subtract 3x from both sides of the equation and then divide both sides by 2. If you follow those instructions to the letter you end up with y=4-3x/2 But for the sake of standardization and to reduce confusion in the long run we put the part with the x first so we have y=-3x/2 + 4. The slope is always the number part of the x term so in this case -3/2