In our last lesson, we introduced the topic of solving linear systems in two variables. We learned how to solve a linear system using graphing. Although we can obtain a solution using graphing, the method is not very practical. In this lesson, we will focus on another method to solve a linear system known as "substitution". The substitution method is most useful when one of the coefficients for one of the variables is either 1 or -1. Show Solving a Linear System using the Substitution Method
Let's look at a few examples. Special Case Linear SystemsIf both variables drop out when solving a system of linear equations:
Linear Systems with No Solution In some cases, we will not have a solution for our linear system. This will occur when we have two parallel lines. This type of system is known as an "inconsistent system". If we are solving our system using the substitution method, we will notice that our variables disappear and we are left with a false statement. Let's look at an example. Linear Systems with Infinitely Many Solutions Another special case scenario occurs when the same equation is presented twice as a system of
equations. In this case, what works as a solution for one equation works as a solution to the other. These equations are known as "dependent equations". Let's look at an example. Skills Check:Example #1 Solve each system using substitution. $$-46x - 19y=-38$$ $$92x + y=2$$ Please choose the best answer. Example #2 Solve each system using substitution. $$6x - 8y=0$$ $$-11x + 15y=19$$ Please choose the best answer. Example #3 Solve each system using substitution. $$27x + 7y=147$$ $$x + y=1$$ Please choose the best answer. Congrats, Your Score is 100% Better Luck Next Time, Your Score is % Try again?
What are the 5 steps in solving equations by substitution?Solving Systems of Equations By Substitution:. Step 1: Rearrange one of the equations to get 'y' by itself. ... . Step 2: Substitute the rearranged equation into its partner. ... . Step 3: Solve for x. ... . Step 4: Substitute the solution for x into either of the initially given equations to find y. ... . Step 5: Write final answer out as a point.. What is the solution of the system using substitution?The substitution method functions by substituting the one y-value with the other. We're going to explain this by using an example. We can substitute y in the second equation with the first equation since y = y. The solution of the linear system is (1, 6).
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