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High School
Algebra
Algebra I
Systems of equations

Recent questions in Systems of equations

Damon Vazquez 2022-09-06

Make a system with 3 equations and 3 unknowns of which the solution space V is spanned by the column vectors: $[\begin{matrix} 1 \\ 0 \\ - 1 \end{matrix}], [\begin{matrix} 1 \\ 3 \\ 0 \end{matrix}]$

engausidarb 2022-09-06

If 𝑎 be the arithmetic mean between 𝑏 and 𝑐, 𝑏 be the geometric mean between 𝑐 and 𝑎 then prove that 𝑐 is the harmonic mean between 𝑎 and 𝑏.

dansleiksj 2022-09-05

Consider the coupled nonlinear system of equations given by
$x^{3} + e^{y} = s \cos x + x y = t$
which we wish to be able to solve uniquely for $(x, y)$ in terms of $(s, t)$ . Show this cannot be done at $(x, y) = (0, 0)$ .

inhiba5f 2022-09-05

For a square matrix $A$ , $A$ is invertible if and only if $A A^{T}$ is

Pavukol 2022-09-04

Stability analysis for ODEs with non constant inputs
${\begin{cases} \dot{x} = I (t) x + x^{2} \\ \dot{y} = x \end{cases}$
where $I (t)$ is a random input (for example).

alexmjn 2022-09-03

A collection of 52 dimes and nickels is worth $4.50. How many nickels are there?

Randall Booker 2022-09-03

Solve this system of equations by substitution:
2x - 4y = -16
y = 3x -1

Beckett Henry 2022-09-03

Use the method of substitution to solve the system.
$3 x - 4 y = 25$
$x^{2} + y^{2} = 25$

alan3885uo 2022-09-01

Use the method of substitution to solve the system.
xy=2
3x-y+5=0

Leroy Gray 2022-09-01

Write Octave statements to solve the following linear system. You don't have to find the final values for x, y, and z.
$6 x - 4 y + z = 3 3 y - 7 = - 4 x + 9 y - 5 z = 5$

Buszmenan 2022-09-01

Huge linear system of equations with powers of $2$ :
$\begin{aligned} (2^{0})^{n} a_{n} + (2^{0})^{n - 1} a_{n - 1} + \dots + (2^{0})^{1} a_{1} & = 4^{0} \\ (2^{1})^{n} a_{n} + (2^{1})^{n - 1} a_{n - 1} + \dots + (2^{1})^{1} a_{1} & = 4^{1} \\ ⋮ \\ (2^{n - 1})^{n} a_{n} + (2^{n - 1})^{n - 1} a_{n - 1} + \dots + (2^{n - 1})^{1} a_{1} & = 4^{n - 1} \end{aligned}$
for $n \geq 2$ . Show that the (unique) solution of this system is when $a_{2} = 1$ and all other variables are zero.

Nailah Jones2022-08-27

Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.

Tara Schultz2022-08-16

Crancichhb 2022-08-07

Solve the system.
4x - 2y- 2z = 5
2x- y - z = 7
-4x + 2y + 2z =6

wendi1019gt 2022-08-03

Solve the following system of equations. If there are no solutions, type "No Solution" for both x and y. If there are infinitely many solutions, type "x" for x, and an expression in terms of x for y.
1 x + 3 y = 8
2 x + 6 y = 16
x =
y =

babibell06cz 2022-08-02

For what value(s) of h is the linear system consistent?
6x1 ? 8x2 = h
?9x1 + 12x2 =?1

Alonzo Odom 2022-07-30

Use eliminatgion to solve each system of equations
(1)2x-3y =-10
3x+2y=-6
(2)3x + 2y = -26
4x - 5y = -4

Darryl English 2022-07-28

If the equation of a circle is $x^{2} + y^{2} = r^{2}$ and the equation of a tangent line is y = mx + b,show that $r^{2} (1 + m^{2}) = b^{2}$

Jadon Melendez 2022-07-28

Solve the system of equations.
2x -y + 3z = 14
x + y - 2z = -5
3x + y - z = 2

Dawson Downs 2022-07-27

Solve the system of equations.
x - 3y + 2z = -11
2x - 4y + 3z = -15
3x - 5y - 4z = 5

In simple terms, systems of equations represent a special set of simultaneous equations where the equation system is used as a finite element. The trick here is to find common solutions, which is exactly what systems of equations solver must achieve. If this does not sound clear to you, take a look at some systems of equations answers below and see those with explanations. The solution will always come in three variables (namely, x, y, and z), which will represent your ordered triple. See systems of equations solutions for more examples of how it works in practice.

Algebra I

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