Solving a System of Equations in Three Variables Find the complete solution of the linear system, or show that it is inconsistent.
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Chapter 10 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Solving a system of equation in three variables Find the complete solution of the linear system, or show that it is inconsistent. {2x+yz=8x+y+z=32x+4z=18}arrow_forwardFind 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_forwardUse any method to solve the nonlinear system. (Order your answers from smallest to largest x, then from smallest to largest y. If there is no solution, enter NO SOLUTION.) x2 + y2 = 6 xy = 1 (x, y) = (x, y) = (x, y) = (x, y) =arrow_forward
- Two algebraic methods to solve a system of linear equations in two variables are the __________ method and the __________ method.arrow_forwardA variable needs to be eliminated to solve the system of equations below. Choose the correct first step. minus, 4, x, minus, 3, y, equals, minus, 33 −4x−3y= −33 minus, 2, x, plus, 3, y, equals, minus, 21 −2x+3y= −21arrow_forwardFind all solutions of the given system of equations and check your answer graphically. [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 - x/3 = 1 x/3 + y = -3 (x, y) = ( )arrow_forward
- The 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_forwardUse technology to solve the system of equations. Express all solutions as decimals, rounded to one decimal place. 2.1x + 0.7y − 1.4z = −2.7 3.5x − 4.2y − 4.9z = 4.6 1.1x + 2.2y − 3.3z = −9.4 (x, y, z) =arrow_forwardSolve the system of equations by using elimination. (If there is no solution, enter NO SOLUTION. Order your answers from smallest to largest x, then from smallest to largest y.) x2 + y2 = 16 x2 − 2y = 8 (x,y)= (x,y)= (x,y)=arrow_forward
- Solve the system of equations by using elimination. (If there is no solution, enter NO SOLUTION. Order your answers from smallest to largest x, then from smallest to largest y.) x2 − y2 = 1 x2 − 2y = 4 (x, y) = (x, y) = (x, y) = (x, y) =arrow_forwardUsing the method of variation of parameters, determine the general solution of the systemarrow_forwardDetermine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5 4 x − 3 4 y = 1 −x + 3 5 y = − 4 5 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =arrow_forward
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