System of Linear Equations - Let’s learn how to solve step-by-step…

How to solve a 2 variable linear system using the elimination / linear combination method and the substitution method.
For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All courses developed and taught by me (experienced and certified math teacher 🤩).
With my courses you CAN reach your math goal! 💪
All Courses - TCMathAcademy....
✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.
TC Math Notes
Pre-Algebra Notes: tabletclass-ma...
Algebra Notes: tabletclass-ma...
Geometry Notes: tabletclass-ma...
Algebra 2 / Trig Notes: tabletclass-ma...

[@jamesmccamish3901]

Thank you, the overview of alternative approaches and the guidance on how to set up and organize the equations is really valuable.

[@johnnolen8338]

The quickest solution is obtained via Cramer's rule, but it is difficult to see why that works. My second choice is elimination but again, it's hard to track all the moving parts. Substitution in this case is straightforward and though somewhat tedious it is also easy:
x + 2y = 1
3x + 4y = - 1
4x + 6y = 0 => y = - 2/3 x.
x + 2(-2/3 x) = 1.
-1/3 x = 1.
x = - 3.
y = - 2/3( - 3) = 2. ◼

[@user-no1lp3lv7x]

Just love your explanation

[@danieldennis9831]

simlify both equations
eq 1 2x-2y=3x-1: -x=2y-1
eq 2 4y-3=-3x-4: 3x=-4y-1
multiply simplified eq 1 by three: -3x=6y-3
subtract simplified eq2
result: 0=2y-4, 4=2y, y=2
solve either eq using substitution (using simplified eq 1)
-x=2(2)-1, -x=4-1, -x=3, x=-3
use other original eq as check: 4(2)-3=-4-3(-3), 8-3=-4+9
5≡5 ... True
Solution: (-3,2)

[@admnner21111]

What will be the equation on the number line graph when we put on the coordinates please? Which equation is the correct one🤔before elimination or after 🤔we need to put both equations please? 🤔or just the eliminated ones?🤔 Tnx?

[@GlobalHealthSI]

Cool. Thanks!

[@GoDemocracy9352]

x= -3 & y= 2

[@thatomofolo452]

👋👋

[@tomtke7351]

magic: 2 unknowns? need 2 equations.

[@kimzlife5993]

Umm kay 😂