Identify the solutions of the systems of equations

Question

1) 4x+6y=1 and y=3-3x

 

2) -3x-4y=2 and 8y=-6x-4

 

3) 3x+2y=4 and 5x-4y=3

 

4) 7x+2y=6 and 6x-2y=6

 

5) 3x-2y=6 and 5x=5-25y

Answer 1

Hi Kimberly,

I will be happy to help you, but this forum is to help you learn how to solve problems not simply for the tutors to do your homework for you.  I will do the first two problems and walk you through the solution.  Then how about you see if you can apply the same techniques to solving the other three. 

 

I kno most kids think "Why do I have to learn this?" Trust me in a world where cashiers cannot make change knowing  how to love these types of problems and the other things you will learn in Algebra this year and next will help you get along better in your career than if you don't learn how to do it.

 

1) 4x+6y=1 and y=3-3x

 

The point of having two equations in two unknowns is using the two equations together to get to one equation in just one unknown which we can then solve.  The two unknowns are of course x and y.   Since the second equation has already solved for y in terms of x, let us substitute it into the first equation for y.

 

4x + 6y = 1  

 

4x + 6(3-3x) =1

 

4x + 18 - 18x = 1

 

-14x = -17

 

so x = 17/14

 

substitute this back into the second equation will solve for y

 

y = 3-3x

 

y = 3 - 3*17/14

 

y = 42/14 - 51/14

 

y = -9/14

 

now we can and should check our answers by plugging the values into the first equation.

 

4x + 6y = 1

 

4(17/14) + 6(-9/14) = 1 , to simplify multiply both sides by 14

 

4*17 - 6*9 = 14

 

68 - 54 = 14

 

14 = 14  QED, which is latin for we just proved ti.

 

I have to go have dinner.  When I get back I will do a second one for you.  Meanwhile why don't you try solving some of the others like I just solved this one.  If you have any questions, please feel free to ask away.

 

Get ready for MARDI GRAS!  It's only a month away!

 

Sincerely,

Ralph K.

 

Answer 2

This is basic straightforward problem Kimberly. 

4x+6(3-3x)=1

4x+18-18x=1

-14x+18-18=1-18

-14x=-17

x=17/14

=> y=3-3*17/14.....