Solving Linear-Quadratic Systems by Substitution
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- Linear-Quadratic Systems Let's say we want to solve a system of equations that is linear AND quadratic. Usually this means one of the equations is linear and another equation is…
By Joshua Siktar, Jonathan Heller, Dani, Caroline K, Anusha Rahman
- (Video) Solving Linear Quadratic Systems Using Substitution by Aaron Tyson In this video, Aaron Tyson goes over how to solve a system of equation using substitution. When lookin…
By Anusha Rahman
- Linear-Quadratic System: Substitution There are many ways to solve linear-quadratic systems of equations. This lesson will explore substitution. When solving a linear-quadratic …
By Anusha Rahman
Problems 25
- Find the solution(s) to the following system by substitution. {y=−3x+8y=x2−4x+2\left\{\begin{matrix}y=-3x+8\\y=x^2-4x+2\end{matrix}\right.{y=−3x+8y=x2−4x+2
- Find the yyy value(s) of the solution(s) to the following system by substitution. {y=2x2+6y=−11x+12\left\{\begin{matrix}y=2x^2+6\\y=-11x+12\end{matrix}\right.{y=2x2+6y=−11x+12
- Find the the solution(s) to the following system by substitution. {y=x2+7y=−6x−2\left\{\begin{matrix}y=x^2+7\\y=-6x-2\end{matrix}\right.{y=x2+7y=−6x−2
- Find the the solution(s) to the following system by substitution. {y=x2−8x+16x=y/2\left\{\begin{matrix}y=x^2-8x+16\\x=y/2\end{matrix}\right.{y=x2−8x+16x=y/2
- Find the the solution(s) to the following system by substitution. {x=y+2y=−1\left\{\begin{matrix}x=\sqrt{y+2}\\y=-1\end{matrix}\right.{x=y+2y=−1
- Solve the following system by substitution. {x=y2−y−3x=y+5\left\{\begin{matrix}x=y^2-y-3\\x=y+5\end{matrix}\right.{x=y2−y−3x=y+5
- The sphere x2+y2+z2=1x^2 + y^2 + z^2 = 1x2+y2+z2=1 has many rational solutions. For instance, start with the point (x,y,z)=(1,0,0)(x,y,z) = (1,0,0)(x,y,z)=(1,0,0), and draw the …
- At what value of kkk do the graphs of y=x2y=x^2y=x2 and y=4x−ky=4x-ky=4x−k intersect at exactly one point?
- This evening a comet is going to cross into the orbit of planet A. The orbit of planet A is the circle x2+y2=10x^2+y^2=10x2+y2=10. The comet is traveling a linear path with the …
- Solve the following system of equations using substitution. {y=x2+3y=x+9\begin{cases} y=x^2+3\\ y=x+9 \end{cases}{y=x2+3y=x+9
- Solve the following system for ttt by solving the 1st equation for sss and substituting the result into the second equation. {5s=t2+st+7s=5+t\begin{cases} 5s=t^2+st+7\\ s=5+t \e…
- Solve the following system for ttt by solving the 1st equation for sss and substituting the result into the second equation. {7s=t2+st+17s=7+t\begin{cases} 7s=t^2+st+17\\ s=7+t …
- Solve the following system for ttt by solving the 1st equation for sss and substituting the result into the second equation. {4=6t2+2ss=2t2+2s\begin{cases} 4=6t^2+2s\\ s=2t^2+2s…
- Two pirate ships are sailing on the same sea. Using longitude and latitude, their trajectories can be mapped to a grid, where xxx and yyy are the ship's coordinates. Ship 1's tr…
- Erin and Kristen are playing a game, tossing balls back and forth. They are trying to toss balls to each other at the same time, in opposite directions, but the balls keep bumpi…
- What is the simplified version, written in standard form, of the equation y=x2+4x+2y=x^2+4x+2y=x2+4x+2 when you substitute x=4y+1x=4y+1x=4y+1 in for xxx?
- What is the simplified version, written in standard form, of the equation y=2x2−x+1y=2x^2-x+1y=2x2−x+1 when you substitute x=3y−1x=3y-1x=3y−1 in for xxx?
- What is the simplified version, written in standard form, of the equation y=2x2+4x−1y=2x^2+4x-1y=2x2+4x−1 when you substitute y=6x2+7x+3y=6x^2+7x+3y=6x2+7x+3 in for yyy?
- How many pizzas should be ordered?
- Find the coordinates of the blue points with the information above.
- Using the information above, find the coordinates of the blue points. x=9x=(y+1)2\begin{array}{rcl} x&=& 9 \\ x &=& (y + 1)^2 \end{array}xx==9(y+1)2
- Using the information above, find the coordinates of the blue coordinates.
- Using the information above, find the coordinates of the green points.
- Using the information above, find the coordinates of the green points.
- Which of the following is a solution (x,y)(x, y)(x,y) to the system of equations below? y=x2−5x−24y=x−8.\begin{align} y &= x^2 - 5x - 24 \\ y &= x - 8. \end{align}yy=x2−5x−24=x…