Use substitution. 2x + 3y = 5 4x – y = 17 use linear combinations: 2x + 3y = 5 4x – y

Use substitution. 2x + 3y = 5 4x - y = 17 use linear combinations: 2x + 3y = 5 4x - y = 17

Related Posts

This Post Has 12 Comments

  1. 2x+3y=5(i)

    5x - 4y=2(ii)

    3y=5-2x

    Y=5-2x/3

    Now, putting the value of Y in ii,

    5x - (5-2x/3)4=2

    15x-20+8x=6

    23x=20

    X=20/23

    Y=75/69

  2.   x = 3, y = 1 OR  (3, 1)

    Step-by-step explanation:

    let 2x + 3y = 9  be [a]   &   y = x − 2 be [b]

    First, lets substitute [b] into [a] and solve for x

       2x + 3( x - 2) = 9

              2x + 3x  = 9 + 6

                       5x = 15

                          x = 3

    Now, since x = 3, we can substitute for x in [b]

           ⇒  y = 3 - 2

                 y = 1

    ∴ the solution for the system of equations is x = 3, y = 1 OR  (3, 1)

  3. i would solve 4x-y =3 for y because  the coefficient for y is 1

    subtract 4x from each side

    -y = -4x+3

    divide by -1

    y = 4x-3

  4. I'll help you get started. To use substitution on the first pair of equations, we want to solve for one of the variables in one of the two equations. It looks like it would be easiest to solve for y in the second equation:
    [tex]4x-y=17[/tex]
    [tex]4x=17+y[/tex]
    [tex]4x-17=y[/tex]

    Now we want to substitute this alternate version of y into the first equation:
    [tex]2x+3(4x-17)=5[/tex].

    I'll let you finish off that first one. The second problem asks to solve the two equations using linear combination. This means we want to add the two equations together and cancel out one of the variables. Again, it's easiest to cancel out the y since one is negative. First we want to take the second equation and multiply by 3 on both sides:
    [tex]3(4x-y)=3(17)[/tex]
    [tex]12x-3y=51[/tex]

    Now we want to add both equations together. Add the left sides and the right sides on their respective sides of the equals sign:
    [tex](2x+3y)+(12x-3y)=5+51[/tex]

    You can finish that one as well. Your answers for both methods will be the same if you do everything right! Let me know if you have more questions

  5. Substitution method is an algebraic method which is used to find the solution of a system of equations, In this method we find the value of one variable in the term of second variable with help of one equation,

    Then substitute this vale in another equation

    Now, Here the given system of equations,

    2x − 3y = 11 (1)

    x + 2y = −5 (2)

    When we see the equations we find that it is easy to find the value of x with help the equation 2, ( Because here the coefficient of x is 1)

    Thus, choosing equation 2 is the good idea,

    From equation (2),

    x = -5 - 2y --- (3)

    By substituting this value in equation (1),

    We get, 2(-5 - 2y) -3y = 11

    -10 - 4y - 3y = 11

    -10 - 7y = 11

    -7y = 21

    y = -3

    By equation (3),

    x = - 5 - 2 × - 3

    x =  - 5 + 6

    x = 1

    Thus, the solution of the given system is x = 1 and y = -3

  6. The given system of equations is

    [tex]2x + 3y = 12[/tex] and

    [tex]x - 2y = 4[/tex]

    From the given set of options, it would be best for Kyle if he takes option C as the first step. That is, "Kyle should solve the second equation for x because x has a coefficient of 1".

    This is because it will make further solution easy. Let us know how.

    The coefficient of x is 1. Thus, x will be represented as: [tex]x=4+2y[/tex] after adding [tex]2y[/tex] to both sides. Now, this can be substituted in the first equation and we can solve for y. Once that is done we can easily solve for x using any of the two equations (whichever is the easiest).

  7. Step-by-step explanation:

    Step 1:  Substitute y from the second equation into the first

    [tex]2x - 3y = -10[/tex]

    [tex]2x - 3(4x) = -10[/tex]

    [tex]2x - 12x = -10[/tex]

    [tex]-10x / -10 = -10 / -10[/tex]

    [tex]x = 1[/tex]

    Step 2:  Substitute the value of x into the second equation

    [tex]y = 4x[/tex]

    [tex]y = 4(1)[/tex]

    [tex]y = 4[/tex]

     [tex](1 , 4)[/tex]

  8. -2x=3y    (we have 9 more) = 9

    -4 = 5  x=-4 =9  as -4+5=1

    -2x=3y = 1

    = +-4 + 4 = 8 + 1 = 9

    y=5  

    As -2x=3y = 1

    = +-4 + 4 = 8 +1 = 9

    + 5 +5 +5 = 15

    Step-by-step explanation:

Leave a Reply

Your email address will not be published. Required fields are marked *