y=3x-5 3x+2y=-19

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sciftw's profile pic

sciftw | High School Teacher | (Level 1) Educator Emeritus

Posted on

This one looks daunting at first because you have two different unknown variables.  In reality though, you only have one.  The y value has been given to you.  It's 3x-5. Plug that into the other equation.

3x + 2(3x-5) = -19

3x + 6x -10 = -19

9x -10 = -19

9x = -9

x = -1

Now take the found x value (-1) and plug it into the y equation.

y = 3(-1) - 5

y = -3 - 5

y = -8

You can check your value for y by going back to the equation that contains both unknown values 3x + 2y = -19

3(-1) + 2(-8) = -19

-3 + -16 = -19

Yep, those values work.  

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

Given

y=3x-5-------------(1)

3x+2y=-19----------(2)

subtract with 5 on both sides of equation (2)

(2)--->  3x+2y -5= -19-5

=>    3x-5+2y=-24

=>    (3x-5)+2y=-24

=>    y+2y=-24

=> 3y=-24

y= -8    <-----answer

so substituting the value of y in equation (1) we get

(1)-------->       y=3x-5

           =>        -8=3x-5

          =>         -8+5=3x

         =>           -3=3x

                          x=-1      <-----answer

so (x,y) =( -1,-8)..................hope this answers helps you ....:)

vamkitten's profile pic

vamkitten | Student, Undergraduate | (Level 1) Honors

Posted on

Y=3x-5

3x+2y=-19

sub Y=3x-5 In 3x+2y=-19 

3x+2(3x-5)=-19

3x+6x-10=-19

9x=-9

x=-1

y=3(-1)-5

  =-8

mcshean's profile pic

Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

With problems like these, they are called systems of equations. The level of this question is particularly easy, considering that there can be over three or four equations in the system, while this one only has two.

Let's take a look at the equation.

y=3x-5

3x+2y=-19

Hmm, so you need to find the value of x and the value of y.

So that's TWO variables. It isn't as hard as you think, because you can use a technique called substitution. In substitution, you can see that y=3x-5. Who says you can't just apply that value to the second equation?

So, if you replace the y in 3x+2y=-19, you get

3x+2(3x-5)=-19

Oh dear, well doesn't this look just terrifying. Worry not! It's simpler than it looks.

Distribute the two on the outside of the parentheses to what is inside of it. So, do 2 * 3x and 2 * 5. Since there is a subtraction sign, these two products will be subtracting from each other. Therefore, 2(3x-5)=6x-10. Add this to the equation (replace 2(3x-5) with the new products from distribution).

3x+6x-10=-19

Simplify. 3x+6x=9x. 

9x-10=-19

There is a subtraction of 10 on the left side of the equation (section of equation on the left of the equal sign). Add 10 to both sides to remove the 10 on the left side and add 10 on the right side, to maintain the law of the equal sign.

9x=-9

We are left with 9x=-9. Since you want to find a whole value of one x, you need to divide both sides by 9.

x=-1. 

-1 is the value of x!

HALT! The problem is not finished yet. With the first equation, y=3x-5, you can now plug in the value of -1 for x.

y=3(-1)-5

3 * -1=-3; -3-5=-8.

y=-8.

-8 is the value of y!

So, if you want to look at this on a cartesian plane, the intersection of these two equations is at (x,y) = (-1,-8).

I hope I helped! Have a wonderful day!

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