Systems of Linear Equations with 3 Variables: Substitution
Read this topicExplanations 4
- If you see a system of equations (such as the one below) that would be very confusing to solve with normal substitution, you can use the Elimination Method. These are our exampl…
By Vivian Loh
- Combine the terms (...a lot) First off: to solve a system of equation with nnn variables using algebraic methods, you need to have at least nnn equations. For example, if you ha…
By Zora Gilbert, MrMXS, Alex Federspiel, Gabi Slizewska, Anusha Rahman
- In both of the following examples by patrickJMT, you will have the chance to walk through examples of how to solve systems of equations with 333 variables, using the process of …
By Alex Federspiel, Anusha Rahman
- Systems of Linear Equations: Substitution with 3 Variables Solving a system of linear equations with 3 variables can seem really overwhelming at first, but with a few steps, you…
By Anusha Rahman
Problems 10
- Solve the system of equations. {x−y+z=−1x−y−2z=4−2x+y−z=2\\\begin{cases}x-y+z&=-1\\x-y-2z&=4\\-2x+y-z&=2\end{cases}⎩⎨⎧x−y+zx−y−2z−2x+y−z=−1=4=2
- Solve the system of equations. {x+y+z=−36x−y+2z= 8x−y+2z=−7\\\begin{cases}x+y+z&=-3\\6x-y+2z&=\ \ \ 8\\x-y+2z&=-7\end{cases}⎩⎨⎧x+y+z6x−y+2zx−y+2z=−3= 8=−7
- Solve the system of equations. {3x+3y+6z=93x−y+z=3x−6y+3z=12\\\begin{cases}3x+3y+6z&=9\\3x-y+z&=3\\x-6y+3z&=12\end{cases}⎩⎨⎧3x+3y+6z3x−y+zx−6y+3z=9=3=12
- Solve the system of equations. {x−3y+2z=12x+2y+z= 43x+y+2z= 6\\\begin{cases}x-3y+2z&=12\\x+2y+z&=\ \ 4\\3x+y+2z&=\ \ 6\end{cases}⎩⎨⎧x−3y+2zx+2y+z3x+y+2z=12= 4= 6
- Solve the system of equations. {4x+2y+z=24x−2y+5z=62x+2y+z=72\\\begin{cases}4x+2y+z&=2\\4x-2y+5z&=6\\2x+2y+z&=72\end{cases}⎩⎨⎧4x+2y+z4x−2y+5z2x+2y+z=2=6=72
- Solve the system of equations. {6x+y+4z=−84y+2x=6−3z4x−y+z=−5\\\begin{cases}6x+y+4z&=-8\\4y+2x&=6-3z\\4x-y+z&=-5\end{cases}⎩⎨⎧6x+y+4z4y+2x4x−y+z=−8=6−3z=−5
- Solve the system of equations. {z+2x+3y=679x+4z=4+5y3x−4+4y=28z\\\begin{cases}z+2x+3y&=67\\9x+4z&=4+5y\\3x-4+4y&=28z\end{cases}⎩⎨⎧z+2x+3y9x+4z3x−4+4y=67=4+5y=28z
- Tim the 8th nods along. He wants to guess c=8c = 8c=8, because the other Tims have guessed different values of ccc. If Tim is correct that c=8c=8c=8, at most how many of the rem…
- Consider the following system of three linear equations with three variables (x,y,z)(x,y,z)(x,y,z). \begin{align} 2x+3&y+z = 10 \ 3x + 2&y + 3z = 10 \ ax + b&y + cz = 10 \end{al…
- Find a quadratic polynomial ppp such that p(0)=0p(0) = 0p(0)=0, p(2)=1212p(2) = \frac{121}{2}p(2)=2121, and p(8)=11p(8) = 11p(8)=11.