10. The equation of the parabola y = ax? + bx + c that passes through the points (-1, 9), (1, 5), and (2, 12). In each of these points, they have given the values for x and y that make the quadratic equation true. Plugging the three points in the general equation for a quadratic, we get a following system of three equations, where the variables stand for the unknown coefficients of that quadratic: c - b+a = 9, b+c+a = 5, 4a + 2b = c = 12 Solve the above system of equations for a, b, c by using Cramer's rule:

Q: I. Find the values of x1, x2, x3 in the system of Linear Equations 2.x, – 6x2 – x3 = -38 | -3x, – Xz…

A: The given system of Linear equations are  2x1-6x2-x3=-38-3x1-x2+7x3=-34-8x1+x2-2x3=-20 To solve…

Q: 11)Give all solutions to the nonlinear system, including non-real complex c (10x2 + y? = 1 %3D a)…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Suppose that the three points (-2, 3), (4, 33), and (-6, -7) lie on the parabola p(x) = ax^2 + bx +…

A:

Q: 7. For what values of k will the system 2z + ky + z = 0 (k - 1)r - y + 2z = 0 4z + y + 4z = 0 have…

A: Determinant be zero for non-trivial  solution

Q: 8. Use any method to find the general solution of the system I' 2 = + [1/₂].

A: We solve by eigenvector method.

Q: 1. Solve the following system of equations by Gauss Jordan Method 2х + у — 2; 4x — у %— — 5 - -

A:

Q: 1. What is the solution in the system 2x – 3y = -1 and x + 5y = 6? A. (1, 1) B. (6, 0) C. (4, 3) D.…

A:

Q: 4. The system x+e -2 =0 y'+e*-2% D0 has a root in the first quadrant, start with x, =1 and y =1…

A:

Q: Find the quadratic function y = ax^2 + bx + c whose graph passes through the given points: (−1,−3),…

A: To determine the solution of the equation.

Q: 7. For what values of k will the system 2x + ky + z = 0 (k – 1)z – y + 2z = 0 4x + y + 4z = 0 have…

A:

Q: Find a solution to the system 3 1 [+] 0-690 = by solving the IVP with initial condition x(t) = -4…

A: Solution

Q: 7. Solve for x, y and z using Gauss-Jordan Elimination 2w + x – 3y – 3z = 4 x + 2y +z = -3 2w – x +…

A:

Q: g system of ec y = =

A:

Q: 1. For the three-part question that follows, provide your answer to each part in the given…

A: NOTE: Refresh your page if you can't see any equations. . the system has exactly one solution when…

Q: Suppose that the three points (1, −5), (−1, 1), and (2, 7) lie on the parabola p(x) = ax 2 + bx + c.…

A: Given The three points (1, −5), (−1, 1), and (2, 7) lie on the parabola p(x) = ax2 + bx + c.

Q: 1 When solved graphically, which system of equations will have exactly one point of intersection? 1)…

A:

Q: Q2: Sketch 3 graphs each containing 3 lines l1, l2, and lz so that on the first graph the the system…

A: For a system of linear equation to have unique solution, all the three lines intersect at only one…

Q: Consider the following linear equations: 2r – y - 6z = -2, I- 5y – z -8, 4r +y - z = 13. Use Gauss…

A:

Q: he figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a =…

A: We creat equation of the flow of traffic X1 = 400 + X2 X1 - X2 = 400.............(1) X4  = 200 +X2…

Q: 15. Solve the following system of equations. SHOW WORK x + 3y + 4z = 13 2x - 3y + 2z = 2 3x- y+ z 8…

A: System of equations  x+3y+4z =13 2x-3y+2z = 2 3x- y + z = 8  To solve the given system of equations

Q: If a, b, c are real numbers and b different from 0, find the relationships between a, b, c and the…

A: Answer

Q: 2x + 4y + 3z = 5 . Use Gauss – elimination to solve the linear system 9x + 6y + 8z = 7 11x + 13y +…

A:

Q: 1 1 Use the substitution u = - and v=– to rewrite the equations in the system in terms of the…

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Q: 6 (2b) Solve the following system of equations for x and y, in R?, by row-reduction. Show the work…

A: The augmented matrix must be  aca+cbdb+d Make zeros in column 1 except the entry at row 1, column 1.…

Q: 1. Y = 5x + 2 2. 5у — 25х + 10 3. 5у — 10x + 10 2у — 10х — 4 | Which pair of equations forms a…

A:

Q: 11. Solve the system using Gauss-Jordan Elimination, by hand. -x+ 2y - 3 3x - y-1 (6)

A:

Q: 5. Solve the following system of non-linear equations 2a2-4ry-y = 0, 2y?+10x-a2-4xy-5 = 0 with ro =…

A:

Q: 12 Which is a solution to the following system of equations? What is the e v y = x + 1 y + 5 = 5x –…

A: Given that : Y = X + 1 and                       Y + 5 = 5X - 2  Find the solution of this equation.…

Q: The equations x+y=6 and y=- -10-9 -8-7-6 -5 -4 -3 -2-10 -10 Determine the solution (s) to the system…

A:

Q: Find a system of two equations in three variables, x1, x2, and x3, that has the solution set given…

A: We have given the parametric representation of the equations that were formed from a augmented…

Q: 17. Solve the following system of equations algebraically. 3x-5y+2z = -S 5x + y+ 6z = 33 -2x +10y-3z…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: 11. In each part, solve the linear system, if possible, and use the result to determine whether the…

A:

Q: 3. Consider the straight line æ + y = 1 and the family of straight lines that pass through the…

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Q: Consider the following system of linear equations 31 + 2y + z = 0 I + y + 2 = 0 2 = 0 with solutions…

A: The given system of equations are non-homogenius type(AX=0).

Q: 10.4 Solve the following system of equations using LU decompo- sition with partial pivoting: 2x, -…

A:

Q: 15 Find the solution for the given system of equations in the form (r, y). -r+y = 8 7x +3y =-16 (-4,…

A: Explanation of the answer is as follows

Q: 1. Consider the linear system i1 = -2px1 + qx2 i2 -qx1 – pgx2 where p and q are unspecified…

A: So, the idea is to put the expected solution of x1 and x2 in the question itself and then compare…

Q: tions, and we conclude that V1(r:) $1(r:) (4.336) Consequently, the solution to the system given by…

A: Given,           4E-17uk+E-4vk=02E-1uk+E-2vk=0                   (4.337a)

Q: 2. Find the general solution of the following linear system: X + 3z = 1 Зх + у = 1 None O (-3t + 1,…

A: We have: x+3z=13x+y=1 Now, we can write it in the form AX=b as : 103310xyz=11 Here, A=103310, X=xyz,…

Q: What relation should the coefficients have so that the system has infinitely many solutions?

A: Let ax+by=c and mx+ny=p are two equations.

Q: х, + х, + х, + 2х, + 7x, 3D -12.35 — 5х, + х, + х, — х, + x, %3D -14.95

A:

Q: 7. For what values of k will the system 2z + ky + z = 0 (k – 1)x – y + 2z = 0 4x + y + 4z = 0 have…

A:

Q: 30. What value of b will make the system y 3x + 2 and y 3.5x+b intersect at the point (2, 8)?

A:

Q: (b) Suppose that the three points (1 - 5), (-1, 1), and (2,7) lie on the parabola p(x) = ax + bx +…

A: Substitute the points in the given equation of the parabola we get 3 linear equations in variables a…

Q: Find a system of two equations in three variables, X,, X2, and x3, that has the solution set given…

A:

Q: If x, y, z E Z, find all ordered triplets (x, y, z) that satisfy the system of equations:

A: We have to find out the all ordered triples that satisfy the given system. The given system of…

Q: 11. Determine the solution to the linear system Ax = b and write it in the form x = x, + X. for 37…

A:

Q: Solve the following system of linear equations by Gramer’s Rule.. [x+y+2z=1 ] [2x –y-z=0 ] [x+2y-z=4…

A: Answer

Q: 2. Find the general solution of the following linear system: X + 3z = 1 3x + y = 1 None O (-3t + 1,…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.