Question

The following system has one solution: x = 2, y = −2, and z = 3. 4x − 2y + 5z = 27 Equation 1 x + y = 0 Equation 2 −x − 3y + 2z = 10 Equation 3 (a) Solve the system provided by Equations 1 and 2. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.)

Answer 1

x = t

y = -t

z = (17-6t)/5

Explanation:

First we will write down Equation 1 and Equation 2

4x-2y+5z = 17------(1)

x + y = 0--------(2)

Since we are asked to express our answer in terms of the parameter t so lets suppose x = t and y = -t

Now substitute the value of x and y in equation (1) we get

4(t) -2(-t) +5z = 17

6t + 5z = 17

5z = 17 -6t

z = (17-6t)/5

hence we get the following answer

x = t

y = -t

z= (17-6t)/5

we can also verify our answer by substituting the values of x ,y and z in any of the two equations above, for example lets substitute these values in equation 1

4(t) -2(-t) + 5((17-6t)/5)) = 17

6t + 17 -6t = 17

6t -6t = 17 -17

0 = 0