Solving Linear-Quadratic Systems by Elimination
Read this topicExplanations 3
- Using the Elimination Method to Solve Linear-Quadratic Systems The elimination method uses addition and subtraction to combine the equations in your system. Think of it like smo…
By Hannah Bonville, Mark Paulson, Alex Federspiel, Joshua Siktar, Jonathan Heller, Caroline K, Anusha Rahman
- A linear-quadratic system of equations is a system of equations where at least one equation has linear terms, and at least one equation has quadratic terms. The "standard" examp…
By Joshua Siktar, Jonathan Heller, Caroline K
- (Video) Using Elimination to Solve Linear-Quadratic Systems of Equations by Anusha Rahman In this lesson, Anusha Rahman goes over how to solve a linear-quadratic system of equat…
By Anusha Rahman
Problems 30
- The system {2y−x=63x−y=7\left \{ \begin{matrix}2y-x=6\\ 3x-y=7\end{matrix} \right.{2y−x=63x−y=7 has a single solution (x1,y1)(x_1,y_1)(x1,y1). Find x1+y1x_1+y_1x1+y1.
- Find the solution(s) to the following system. {−4y=x2−2x+3y=12x−1\left \{ \begin{matrix}-4y=x^2-2x+3\\ y=\frac{1}{2}x-1\end{matrix} \right.{−4y=x2−2x+3y=21x−1
- The equations below model the expected attendance at Movie A and Movie B for the first week that Movies A and B are out. If xxx represents the day of the week (with x=1x=1x=1 co…
- Find the solution(s) to the following system using elimination. {16=4x−2y20=x2+3x−y\left \{ \begin{matrix}16=4x-2y\\ 20=x^2+3x-y\end{matrix} \right.{16=4x−2y20=x2+3x−y
- Suppose you begin solving this system with elimination: {y=66x−17y=−12x2+8x−22\left \{\begin{matrix}y=66x-17\\y=-\frac{1}{2}x^2+8x-22\end{matrix}\right.{y=66x−17y=−21x2+8x−22 …
- What is the maximum possible number of intersections of a circle with a parabola?
- What is the maximum possible number of intersections of two distinct circles?
- What is the maximum possible number of intersections of two distinct parabolas with vertical axes of symmetry?
- Solve the following system through elimination: {4x2+x+3y=183x+9y=6\begin{cases} 4x^2+x+3y=18\\ 3x+9y=6 \end{cases}{4x2+x+3y=183x+9y=6
- Solve the following system of equations through elimination: {y−x2=−16y−2x=−8\begin{cases} y-x^2=-16\\ y-2x=-8 \end{cases}{y−x2=−16y−2x=−8
- Solve using elimination: {y−2x2=−16y−2x=−16\begin{cases} y-2x^2=-16\\ y-2x=-16 \end{cases}{y−2x2=−16y−2x=−16
- Solve the following system of equations using the elimination method: {2y−4x=2y=2x2−3\begin{cases} 2y-4x=2\\ y=2x^2-3 \end{cases}{2y−4x=2y=2x2−3
- Album A sales can be represented by the equation: y=12x2−2x+4.y=\frac{1}{2}x^2-2x+4.y=21x2−2x+4. Sales of the greatest hits album can be represented through the linear equation…
- It's the fourth quarter of the state championship game. Your team is down by one and your kicker needs to kick a field goal to win the state title. When the kicker kicks the bal…
- Solve using elimination: Zen is a photographer and she is always on the hunt for the best views. One day she hears about a mountain that has one of the most beautiful views of t…
- Solve the following system of equations using elimination: {2y=9x+76y=−34(4x−3)2\begin{cases} 2y=9x+7\\ 6y=-\frac{3}{4}(4x-3)^2 \end{cases}{2y=9x+76y=−43(4x−3)2
- Solve the following system of equations through elimination:{y=−x+14y=−34(4x2−4)\begin{cases} y=-x+1\\ 4y=-\frac{3}{4}(4x^2-4) \end{cases}{y=−x+14y=−43(4x2−4)
- Solve using elimination: {4y=15(x−5)28y=28−5x\begin{cases} 4y=\frac{1}{5}(x-5)^2\\ 8y=\frac{2}{8}-5x \end{cases}{4y=51(x−5)28y=82−5x
- Solve using elimination: A line with a slope of 444 passes through the point (−1,−6)(-1,-6)(−1,−6). This line intersects the parabola represented by the following equation: y=−1…
- Solve using elimination: A line with a slope of 333 passes through the point (−2,−6)(-2,-6)(−2,−6). This line intersects the parabola represented by the following equation: y=−6…
- What are the coordinates of your house?
- Find all solutions to this system of equations: {y=x2+2x+1(1)y=x2+2x−1(2)\begin{cases} y=x^2+2x+1 \quad (1)\\ y=x^2+2x-1 \quad (2) \end{cases}{y=x2+2x+1(1)y=x2+2x−1(2)
- Solve for the non-zero xxx value using elimination: y=mxy=ax2\begin{array}{rcl} y &=& mx \\ y &=& ax^{2} \end{array}yy==mxax2 mmm and aaa are constants.
- Solve for the non-zero xxx value using elimination: y=−mxy=ax2\begin{array}{rcl} y &=& -mx \\ y &=& ax^{2} \end{array}yy==−mxax2 mmm and aaa are non-zero constants.
- Solve for xxx using elimination. y=(x−a)2−y=2ax−2a2\begin{array}{rcl} y &=& (x-a)^2 \\ -y &=& 2ax -2a^2 \end{array}y−y==(x−a)22ax−2a2 aaa is a real constant.
- Using elimination solve for the non-zero value of xxx. y=(x+a)(x+b)y=ab\begin{array}{rcl} y &=& (x+a)(x+b) \\ y &=& ab \end{array}yy==(x+a)(x+b)ab aaa and bbb are real consta…
- Using elimination solve for the non-zero value of xxx. y=(x−a)(x−b)y=ab\begin{array}{rcl} y &=& (x-a)(x-b) \\ y &=& ab \end{array}yy==(x−a)(x−b)ab aaa and bbb are real consta…
- If you were solving the system of equations below using elimination, which step would most quickly lead you to eliminating y?y?y? y=x2+bx+cy=mx+k\begin{array}{rcl} y &=& x^2 + b…
- Suppose ......... a≠ba≠−ba and b are real constants.\begin{array}{c} \begin{array}{rcl} a &\ne& b \\ a &\ne& -b \end{array} \\ a \text{ and } b \text{ are real constants.} \end{…
- 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…