Question

There are three ways of solving systems of linear equations: graphing, substitution, and elimination. This week we are studying substitution and elimination. Explains in detail how to solve a problem using either of these two methods. You can find a problem to solve in your text book or on the internet. Show your step-by-step solution using one of the two methods. Make sure to include how you will check your solution.

Answer 1

understanding solving system of equations by elimination method

in elimination method we try to eliminate any one variable by adding up the two equations

the variable we wish to eliminate must have same coefficients and opposite signs

lets take an example

equation 1 : x - 2y = 10

equation 2 : x + y = 2

so, we will be eliminating y , as the coefficient of y is different in both the equations

we multiply equation 2 by 2 to make the coefficinets of y equal

( x+y = 2) * 2

2x + 2y = 4

now adding equation 1 to it

2x + 2y = 4

x - 2y = 10

--------------------

3x = 14

x = 14/3

plugging the value of x into either equation to find y

x + 14/3 = 2

x = 2 - 14/3

x = -8/3

hence, solutions are

x = - 8/3 , y = 14/3

plugging each solution into the equation to verify

x + y = 2

- 8/3 + 14/3 = 2

6/3 = 2

2 = 2

hence, solution is correct