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Chapter 1: Q1E (page 5)

in exercises 1 through 10, find all solutions of the linear systems using elimination.Then check your solutions

x+2y=12x+3y=1

Short Answer

Expert verified

The solution of system of equations isx=-1,y=1x=-1,y=1

Step by step solution

01

Step 1:Transforming the system

To get the solution, we will transform the value of x,y鈩�.

x+2y=12x+3y=1Into the formx=....y=....

02

Eliminating the variables.

In the given system of equations, we can eliminate the variables by adding or subtracting the equations.

In this system, we can eliminate the variable xfrom first equation. First of all multiply the first equation by 2.

2x+4y=22x+3y=1

Now subtract the first equation from the second equation.

2x-2x+4y-3y=2-12x+3y=1=y=12x+3y=1

Now put the value of y which is in first equation to the second equation.

y=12x+3(1)=1=y=12x=1-3=y=1x=-1

03

Checking the solution.

Now check the solution by putting the value of x and y in the given system of equation.

2-1+41=2?2-1+31=1?鈬�-2+4=2?-2+3=?1鈬�2=21=1

Hence, the solution of the given system isx=-1,y=1

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Most popular questions from this chapter

in exercises 1 through 10, find all solutions of the linear systems using elimination.Then check your solutions.

4.2x+4y=23x+6y=3

a. Using technology, generate a random matrix A. (The entries may be either single-digit integers or numbers between 0 and 1 , depending on the technology you are using.) Find rref(A). Repeat this experiment a few times.

b. What does the reduced row-echelon form of most3脳3 matrices look like? Explain.

What are the signs of the determinants of the principal submatrices of a negative definite matrix? See Theorem 8.2.5.

In Exercises 57 through 61, consider a quadratic form q on R3with symmetric matrix A, with the given properties. In each case, describe the level surface q(x鈬赌)=1geometrically.

60. qis indefinite and det A>0.

Question:Solve the linear system

|y+z=aX+z=bx+y=C|, where a,b andcare arbitrary constants.
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