Solving Quadratic Systems by Substitution or Elimination
Read this topicExplanations 3
- How to solve simultaneous equations? Solving simultaneous equation is a basic skill in solving various kind of problems. One of the ways of doing this is by substitution. For ex…
By Hoo Zhi Yee, Victor Wang
- (Video) Solving Nonlinear Systems with Substitution by ThinkwellVids Here's a video by ThinkwellVids showing you how to solve a system of nonlinear equations by using substituti…
By Alex Federspiel, Jonathan Heller
- (Video) Solving Nonlinear Systems with Elimination by ThinkwellVids Here's a video by ThinkwellVids showing you how to solve a system of nonlinear equations by eliminating a var…
By Alex Federspiel, Jonathan Heller
Problems 25
- List the values of yyy for which the system {x2+y2−25=0x2−4y−4=0\begin{cases} x^2+y^2-25=0 \\ x^2-4y-4 = 0 \end{cases}{x2+y2−25=0x2−4y−4=0 can have a solution (x,y)(x,y)(x,y).
- Solve the system of nonlinear equations by eliminating. {y=x2+7x−1312 x+3y=16\\\begin{cases}y=x^2+7x-13\\\frac12\ x+3y=16\end{cases}{y=x2+7x−1321 x+3y=16
- Solve the system of nonlinear equations by eliminating. {y=5x2−18x−y=4\\\begin{cases}y=5x^2-1\\8x-y=4\end{cases}{y=5x2−18x−y=4
- Solve the system of nonlinear equations by eliminating. {2x2−7y=158x−5=7y\\\begin{cases}2x^2-7y=15\\8x-5=7y\end{cases}{2x2−7y=158x−5=7y
- Suppose Sudan finds his soulmate on Tinder. She loves long walks in the meadows, and other rhino activities. Furthermore, assume a rhino only gives birth once a year. How many y…
- Two friends are running in the field to get ready for a race. They are each running a different track. Just to spice it up, Joel is running in circles and Lynn is running in a s…
- A circle is defined as x2+y2=25x^2+y^2=25x2+y2=25, and a line is defined as y=2x+5y=2x+5y=2x+5. At what point(s) do these intersect? Select all correct answers.
- {y=x2+11x−10y=7x−5\begin{cases} y&=x^2+11x-10\\y&=7x-5\end{cases}{yy=x2+11x−10=7x−5 Find the solutions to this system of equations. Select all correct answers.
- {x2+(y−5)2=25y=x2\begin{cases}x^2+(y-5)^2=25\\y=x^2\end{cases}{x2+(y−5)2=25y=x2 The system of equations includes a circle with radius 555 centered on (0,5)(0,5)(0,5), and a par…
- {x2−y=5y=3x−1\begin{cases}x^2-y=5\\ y=3x-1 \end{cases}{x2−y=5y=3x−1 Find the crossing point(s) of these two functions. Select all correct answers.
- Find the point(s) of intersection of the circle x2+y2=40x^2 +y^2 =40x2+y2=40 and the line y=2xy=2xy=2x.
- You kick a soccer ball up a hill that can be expressed as the equation y=7xy=7xy=7x. The soccer ball follows the path y=−x2+7x+4y=-x^2+7x+4y=−x2+7x+4. Where does the soccer ball…
- Find the solution(s) to this system of equations. Select all correct answers. {y=x2−3x−15y=2x−1\begin{cases} y&=x^2-3x-15 \\y&=2x-1\end{cases}{yy=x2−3x−15=2x−1
- Find the intersection(s) of these two equations, where yyy is positive. {4x−y2=8y2=3x−1\begin{cases}4x-y^2=8\\ y^2=3x-1 \end{cases}{4x−y2=8y2=3x−1
- Find the intersection(s) of these two equations. {x2+y2=9x−y=3\begin{cases}x^2+y^2=9\\ x-y=3 \end{cases}{x2+y2=9x−y=3
- Find the intersection of these two equations. {4x3+7=y−2y=5\begin{cases}4x^3+7=y-2\\ y=5 \end{cases}{4x3+7=y−2y=5
- Find the point(s) of intersection between the line y=3x+1y=3x+1y=3x+1 and the parabola y=x2−3y=x^2-3y=x2−3.
- Find the point(s) of intersection between the line −x=y−1-x= y-1−x=y−1 and the parabola y=x2+x−2y=x^2+x-2y=x2+x−2.
- Find the number of real solutions for the system: {y=x+8y=−x2\begin{cases} y&=x+8\\y&=-x^2\end{cases}{yy=x+8=−x2
- Find the points of intersections for the system: {2x2−y2−8=0−y2+x2+6=0\begin{cases} 2x^2-y^2-8=0\\-y^2+x^2+6=0\end{cases}{2x2−y2−8=0−y2+x2+6=0
- Solve the following system of equations: {y=x2+4x+36y=x2−2x\begin{cases} y&=x^2+4x+36\\y&=x^2-2x\end{cases}{yy=x2+4x+36=x2−2x
- Solve the following system using substitution: {y=x2+7x+100y+10x=30\begin{cases} y=x^2+7x+100 \\y+10x=30\end{cases}{y=x2+7x+100y+10x=30
- Solve the following system using elimination: {y=x2−x−90y−30=x\begin{cases} y=x^2-x-90 \\y-30=x\end{cases}{y=x2−x−90y−30=x
- Find, approximately, the points of intersections for the system: {y=x2−10x+3y=5(x−3)\begin{cases} y=x^2-10x+3 \\y=5(x-3)\end{cases}{y=x2−10x+3y=5(x−3)
- Find the points of intersections for the system: {2y+4=xy+x2=4\begin{cases} 2y+4=x \\y+x^2=4\end{cases}{2y+4=xy+x2=4