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.)
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
