Elimination by Multiplication - Examples & Practice
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- Using Multiplication for Elimination in Systems of Linear Equations Earlier, we saw how to solve systems of linear equations with graphing (looking at the points where the two f…
By Hannah Bonville, Zora Gilbert, Christine, Alex Federspiel, Sarah Walker, Joshua Siktar, Caroline K, Jonathan Heller, Anusha Rahman
- Multiply for Elimination Some systems can't be solved with only adding and subtracting for elimination. These systems require our old friend, multiplication. You can multiply te…
By Sarah Walker, Victor Wang, Alex Federspiel, Jonathan Heller, Caroline K, Anusha Rahman
- (Video) Solving a System of Equations Using the Elimination Method by mathman1024 This video by mathman1024 looks at elimination with multiplication. Summary He looks at the fol…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
Problems 39
- If −9y+4x−20=0-9y+4x-20=0−9y+4x−20=0 and −7y+16x−80=0,-7y+16x-80=0,−7y+16x−80=0, find the value of 10x+y10x + y10x+y.
- If −5x−3y−9=0-5x-3y-9=0−5x−3y−9=0 and 4x−18y−54=0,4x-18y-54=0,4x−18y−54=0, find yyy.
- Solve the following system of equations. {4x+2y=82x+y=4\begin{cases} 4x+2y=8\\ 2x+y=4 \end{cases}{4x+2y=82x+y=4
- If −15x−9y−27=0-15x-9y-27=0−15x−9y−27=0 and 8x−36y−108=0,8x-36y-108=0,8x−36y−108=0, find xxx.
- If x+2y=14x+2y=14x+2y=14 and x−3y=9,x-3y=9,x−3y=9, find 10x+y10x+y10x+y.
- Solve the following system of equations. {7x+9y=510−14x=18y\begin{cases} 7x+9y=5\\ 10-14x=18y \end{cases}{7x+9y=510−14x=18y
- Solve the following system of equations. 5x−7y=1710x−14y=8\begin{gather}5x-7y=17\\ 10x-14y=8 \end{gather}5x−7y=1710x−14y=8
- Does this system of equations have infinitely many solutions? 28y−21x=−5628y-21x=-5628y−21x=−56 4.5x−6y=124.5x-6y=124.5x−6y=12
- Does this system of equations have infinitely many solutions? 4x+5y=134x+5y=134x+5y=13 12x+15y=2612x+15y=2612x+15y=26
- Which value of aaa makes the system of equations have infinitely many solutions? 4x−5y=164x-5y=164x−5y=16 16x−20y=a16x-20y=a16x−20y=a
- Does the system of equations have infinitely many solutions? 9x−6y+15z=219x-6y+15z=219x−6y+15z=21 21x−14y+35z=4921x-14y+35z=4921x−14y+35z=49 18x−12y+30z=4218x-12y+30z=4218x−12y+…
- Does this system of equations have a solution? 9x−6y=129x-6y=129x−6y=12 21x−14y=2821x-14y=2821x−14y=28
- Which of the following values of aaa makes the system of equations have no solution? 6x+3y=246x+3y=246x+3y=24 4x+2y=a4x+2y=a4x+2y=a
- Does the system of equations have a solution? 4x−3y+6z=124x-3y+6z=124x−3y+6z=12 −5x+12y+2z=21-5x+12y+2z=21−5x+12y+2z=21 12x−9y+18z=3012x-9y+18z=3012x−9y+18z=30
- Does the system of equations have a solution? 6x−3y=96x-3y=96x−3y=9 4x+y=34x+y=34x+y=3
- Does this system of equations have a solution, no solution, or infinitely many solutions? 83x+4y=323\frac{8}{3}x+4y=\frac{32}{3}38x+4y=332 54x+158y=5\frac{5}{4}x+\frac{15}{8}y…
- A school club has 808080 members. There are 999 times as many boys in the club than there are girls. How many girls are in the club?
- Solve the system. x+y=3x+y=3x+y=3 x−3y=1x-3y=1x−3y=1
- What values can you multiply the top equation by before using addition or subtraction (for elimination)? 5x+4y=125x+4y=125x+4y=12 12x+6y=2412x+6y=2412x+6y=24
- Solve the following system. 10x+8y=2410x+8y=2410x+8y=24 12x+6y=2412x+6y=2412x+6y=24
- 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.
- Suppose that 2x+3y=72x + 3y = 72x+3y=7. What is the value of 4x+6y4x + 6y4x+6y?
- Find the value of aaa so that the following system of linear equations has infinitely many solutions. 4x+18y=124x + 18y = 124x+18y=12 10x+ay=3010x + ay = 3010x+ay=30
- The following system of linear equations has infinitely many solutions. 2x+3y=52x + 3y = 52x+3y=5 ax+by=8ax + by = 8ax+by=8 Find aaa and bbb.
- Find the value of aaa that makes this system of linear equations have infinitely many solutions: 3x+2y=a4y+6x+8=0\begin{align} 3x + 2y &= a \\ 4y + 6x + 8 &= 0 \end{align}3x+2y4…
- The sequence a0a_0a0, a1a_1a1, a2a_2a2, …\ldots… satisfies the recurrence equation an=2an−1−2an−2+an−3a_n = 2 a_{n-1} - 2 a_{n - 2} + a_{n - 3}an=2an−1−2an−2+an−3 for eve…
- What coefficient could we multiply the first equation by in the following system of equations in order to more easily eliminate the yyy variable to solve the system? 3x+y=73x + …
- Ezra, Sarah, and Michelle decide to go running through their neighborhood along different paths. They all plan to meet at one specific point in town. Sarah's path follows the li…
- Rewrite the following statements as a system of equations. Then solve for xxx and yyy using elimination. The sum of three times a number, xxx, and one third a different number, …
- Solve the following system of equations by using elimination. 3x−6y=63x-6y = 63x−6y=6 −2x+3y=−5-2x+3y = -5−2x+3y=−5 12x+4y=6\frac{1}{2}x+4y = 621x+4y=6
- Solve the following system of equations. {5x+5y=204x+2y=12−32x+2y=1\begin{cases} 5x+5y=20\\ 4x+2y=12\\ -\frac32x+2y=1 \end{cases}⎩⎨⎧5x+5y=204x+2y=12−23x+2y=1
- Solve the following system of linear equations. {21x−7y=−42−4x+2y=4\begin{cases} 21x-7y=-42\\ -4x+2y=4 \end{cases}{21x−7y=−42−4x+2y=4
- Solve for aaa and bbb. {2(a+b)=4a−b=1\begin{cases} 2(a+b)=4\\ a-b=1 \end{cases}{2(a+b)=4a−b=1
- What is the value of x2+y2x^2+y^2x2+y2? {xy=5(x+y)2=20\begin{cases} xy=5\\ (x+y)^2=20 \end{cases}{xy=5(x+y)2=20
- Solve the following system of equations. {−6x+3y=152x−4y=−2621x−24y=−147\begin{cases} -6x+3y&=15 \\ 2x-4y&=-26 \\ 21x-24y&=-147 \end{cases}⎩⎨⎧−6x+3y2x−4y21x−24y=15=−26=−147
- Solve the following system of equations. {−43x+2y=18−2x+3y=27103x−5y=−45\begin{cases} -\frac{4}{3}x+2y=18 \\ -2x+3y=27 \\ \frac{10}{3}x-5y=-45 \end{cases}⎩⎨⎧−34x+2y=18−2x+3y=2…
- Solve for x,yx,yx,y: {x−2y=122x−y=5\begin{cases} x-2y=12\\ 2x-y=5 \end{cases}{x−2y=122x−y=5
- Solve for x,yx,yx,y. {x=55x−y=22\begin{cases} x=5\\ 5x-y=22 \end{cases}{x=55x−y=22
- Solve for x,yx, yx,y. {2(x−y)=524x−2y=1\begin{cases} 2(x-y) = \frac{5}{2}\\ 4x-2y = 1 \end{cases}{2(x−y)=254x−2y=1