Systems of Linear Equations with Infinite Solutions - Examples
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Problems 19
- 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
- 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
- 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+…
- If a system of equations with variables xxx and yyy has infinitely many solutions, does this mean any xxx and yyy will solve the system?
- Does this system of equations have a solution? 9x−6y=129x-6y=129x−6y=12 21x−14y=2821x-14y=2821x−14y=28
- 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…
- 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…
- What could the second equation be in the below system of linear equations so that the system has infinitely many solutions? 2x+5y=212x + 5y = 212x+5y=21
- What are the conditions necessary for a system of equations to have infinitely many solutions?
- If the following system of equations has infinitely many solutions, what must the relationship between aaa and bbb be? 2x+ay=142x + ay = 142x+ay=14 x+by=7x + by = 7x+by=7
- Which of the following is not a solution to the following system of equations? 3x+4y=83x + 4y = 83x+4y=8 32x+2y=4\frac{3}{2}x + 2y = 423x+2y=4
- What does the relationship between aaa and bbb have to be for the following system of equations to have infinitely many solutions? x−8y=ax - 8y = ax−8y=a 3x−24y=b3x - 24y = b3x−…
- What does the value of aaa have to be for the following system of equations to have infinitely many solutions? 2x+ay=32x + ay = 32x+ay=3 8x+(2a−1)y=128x + (2a - 1)y = 128x+(2a−1…
- What will the graph of the following system of equations look like? 4x−7y=24x - 7y = 24x−7y=2 8x−14y=48x - 14y = 48x−14y=4