For Exercises 41-56, solve the system by the Gauss-Jordan method. For system that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent.
55.
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Intermediate Algebra
- Find all solutions of the given system of equations and check your answer graphically. HINT [First eliminate all fractions and decimals.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).) x 2 − y 3 = 1 x 5 + y = −3 (X,Y)=arrow_forwardThe number of new users y (in millions) for a certain website between August 2008 and May 2009 can be modeled by the equation y=ax2+bx+c, where x represents the age of the user. Using the ordered pair solutions (15,1), (35,8),and (55,5), create a system of linear equations in three variables for a, b, and c. Do this by substituting each ordered pair solution into the model, creating an equation in three variables. Solve the resulting system to find the coefficients of the model. Then use the model to predict the number of new users for the website who were 40 years old.arrow_forwardA system of linear equations can't have exactly two solutions. Why?(a) If (x, y, z) and (X, Y, Z) are two solutions, what is another solution?(b) If 25 planes meet at two points, where else do they meet?arrow_forward
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- Find all solutions of the given system of equations and check your answer graphically. HINT [First eliminate all fractions and decimals.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).) x 4 − y 3 = 1 x 5 + y = −3arrow_forwardFrom 5 methods of solving systems of linear equations that you have learnt, which methods will not give an exact solution? Why?arrow_forwardElizabeth and her children went into a grocery store and she bought $14 worth ofapples and bananas. Each apple costs $1.75 and each banana costs $0.70. She bought6 more bananas than apples. Graphically solve a system of equations in order todetermine the number of apples, a, and the number of bananas, y, that Elizabeth ybought.arrow_forward
- Find all solutions of the given system of equations and check your answer graphically. HINT [First eliminate all fractions and decimals.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).)0.2x + 0.1y = 0.60.4x − 0.4y = 1.6(x, y) =arrow_forwarda system of linear equations reduces to "0=0" how many solutions does the possess?arrow_forwardSolve the system of equations by any method. 3x−4y+2z =−22 (1) 2x+4y+z =18 (2) 2x+3y+5z =21 (3) Enter the exact answer as an ordered triple, (x,y,z).arrow_forward
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