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Chapter 1: Q5E (page 5)

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

5.2x+3y=04x+5y=0

Short Answer

Expert verified

The solution of system of equation isx=0,y=0

Step by step solution

01

Step 1:Transforming the system

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

2x+3y=04x+5y=0Into 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 from equation 1. First of all multiply the first equation by 2.

4x+6y=04x+5y=0

Now subtract the equation 1 from the equation we get.

4x-4x+6y-5y=0-04x+5y=0=y=04x+5y=0

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

y=04x+5(0)=0=y=04x=0=y=0x=0

Hence, we get the value of x and y is0,0

03

Checking the solution

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

2(0)+3(0)=04(0)+5(0)=0

Hence, the solution of the system of equations isx=0,y=0

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Most popular questions from this chapter

Determine whether the statements that follow are true or false, and justify your answer.

19. There exits a matrix A such thatA[-12]=[357]

a. Write the system in vector form.

|x+2y=73x+y=11|

b. Use your answer in part (a) to represent the system geometrically. Solve the system and represent the solution geometrically.

Find the circle that runs through the points (5,5),(4,6),and (6,2). Write your equation in the forma+bx+cy+x2+y2=0. Find the centre and radius of this circle.

Find the polynomial of degree 3 [a polynomial of the formf(t)=a+bt+ct2+dt3] whose graph goes through the points (0,1),(1,0),(-1,0)and (2,-15). Sketch the graph of this cubic.

a. Find all solutionsx1,x2,x3,x4 of the system .

x2=12(x1+x3),x3=12(x2+x4)

b. In partrole="math" localid="1659677484607" (a) , is there a solution with x1=1andx4=13 ?
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