Question

Expeess x y

​
−x 2
​
, and x y
​
in terms of the borameter to 2x 1
​
+x 2
​
−a 2
​
−5
4x 1
​
+2x 3
​
=12
−2x 1
​
+2x 2
​
−16x 1
​
=−9
(x 1
​
x∣i∣x)=(x)
​
Solve the system of linear equations. (Enter your answers a express x 1
​
,x 2
​
, and x 3
​
in terms of the parameter t.) 2x 1
​
+x 2
​
−4x 3
​
=
4x 1
​
+2x 3
​
=
−2x 1
​
+3x 2
​
−16x 3
​
=
(x 1
​
,x 2
​
,x 3
​
)=(3,−1,0
​
5
12
−9
x
​
Solve the system of flnear equations. (Enter your answers as a comma-separated ilist, If there is ne sohition, enter no scuumon. If the system has an infinite humber of solutions, expresi x 1
​
,x 2
​
, and x 3
​
in terms of the paramater t 1
​
) 2x 1
​
+x 2
​
−4x 3
​
=5
4x 1
​
+2x 3
​
=12
−2x 1
​
+3x 2
​
−16x 3
​
=−9
(x 1
​
,x 2
​
,x 3
​
)=(
​

Answer 1

To solve the system of linear equations, use the method of substitution. Solve one equation for one variable and substitute that expression into the other equations. Solve the resulting system of equations to find the values of the variables in terms of the parameter t.

Step-by-step explanation:

To solve the system of linear equations, we can use the method of substitution. We'll solve one equation for one variable and substitute that expression into the other equations. Let's solve for x1 in the second equation:

4x1 + 2x3 = 12

=> 4x1 = 12 - 2x3

=> x1 = 3 - (1/2)x3

Now we'll substitute this expression for x1 into the other equations:

2(3 - (1/2)x3) + x2 - 4x3 = 5

=> 6 - x3 + x2 - 4x3 = 5

=> x2 - 5x3 = -1

3 - (1/2)x3 + 3x2 - 16x3 = -9

=> 3x2 - (33/2)x3 = -12

Now we have a system of two equations in two variables (x2 and x3). We can solve this system to find x2 and x3 in terms of the parameter t. From the first equation, we have x2 = 5x3 - 1. Substituting this expression into the second equation gives: 3(5x3 - 1) - (33/2)x3 = -12. Solving this equation will give us the values of x3 and x2 in terms of t.

Learn more about Solving systems of linear equations