Next Lesson: Word problems that lead to simultaneous equations It really isnt hard, but it takes good organization skills. Here is the solution: x = 2, y = 3, z = 4. Solving 3 x 3 systems of equations works a lot like the 2 x 2 method of elimination - with a little substitution mixed in. To solve for z, substitute x = 1 in equation 5): 3 + zįinally, to solve for y, substitute these values of x and z in one of the original equations say equation 1): 1 + y + 3Īlways verify the solution by plugging the numbers into each of the three equations. Next, multiply equation 2) by 2, and add it to 3): 2') 1)Įliminate y, for example, from equations 1) and 2, and then from equations 2) and 3). To solve for y, let us substitute x = 1 in equation 4): 3 + 4 yįinally, to solve for z, substitute these values of x and y in one of the original equations say equation 1): 1 + 2 − z We will multiply equation 5) by −4, and add it to equation 4): 5')
We now solve equations 4) and 5) for x and y. We will call the resulting equation 1' ("1 prime") to show that we obtained it from equation 1): 1') Next, we will eliminate z from equations 1) and 2). We will first eliminate it from equations 1) and 3) simply by adding them.
The strategy is to reduce this to two equations in two unknowns.ĭo that by eliminating one of the unknowns from two pairs of equations: either from equations 1) and 2), or 1) and 3), or 2) and 3).įor example, let us eliminate z. Solve this system of three equations in three unknowns: 1)
0 kommentar(er)
