Step-By-Step-Math: Solve y = 2x + 1 and 3x + y = 11 | Systems of Equations by Substitution
Solve y = 2x + 1 and 3x + y = 11 | Systems of Equations by Substitution Step by Step
Learning Target: I can solve a system of two linear equations using substitution
What You'll Learn
- Isolate a variable in one equation
- Substitute into the second equation
- Solve and verify the ordered pair
Key Terms
system of equations, substitution, solution, ordered pair, linear equation
Standards Alignment
- CCSS.MATH.CONTENT.HSA.REI.C.6: Solve systems of linear equations exactly
Math Practices
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP6: Attend to precision
Chapters
- 0:00 How do you solve a system of equations?
- 0:07 What is the substitution method?
- 0:14 How do you identify which variable to isolate?
- 0:21 How do you substitute into the second equation?
- 0:28 How do you remove parentheses?
- 0:35 How do you combine like terms?
- 0:44 How do you isolate the variable?
- 0:54 How do you solve for x?
- 1:06 How do you substitute back to find y?
- 1:18 What is an ordered pair?
- 1:26 How do you verify your solution?
- 1:36 What is the final answer?
▶ Click to Read Full Transcript
[00:00] Let's solve this system of equations step by step. We are given two equations. Together, they form a system. We are looking for one ordered pair that makes both equations true.
[00:07] The first equation already tells us what y equals. That makes substitution a good strategy because we can replace y in the second equation.
[00:14] Here is the second equation. We are about to replace y with 2x plus 1.
[00:21] Every time we see y, we replace it with parentheses around 2x plus 1.
[00:28] Now remove the parentheses. Since there is only addition, nothing changes sign.
[00:35] Three x plus two x equals five x. Now we have a one-variable equation.
[00:44] Subtract one from both sides to isolate the x term.
[00:54] Divide both sides by five to solve for x.
[01:06] Now substitute x equals 2 back into the first equation and simplify step by step. Notice that we use parentheses to show the order of operations. Always feel free to pause the video and try it on your own.
[01:18] The solutions are two and five. We use the convention of x first, y second. This is called an ordered pair - our solution is the ordered pair, or point, two, five.
[01:26] Always check your solution in both equations. We check by plugging the ordered pair values into both equations. Since both are true, our answer is correct.
[01:36] I hope you found this helpful along your journey to discovering the joy in mathematics. This has been Mister Marx AI. Until next time, keep up the good work!
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