♡Solve by using system of equations and substatuion-3x – y = -13x + 2y = 6*Show work! ​



Solve by using system of equations and substatuion

-3x - y = -13
x + 2y = 6

*Show work! ​

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  1. 60 ml of 40% saline and 90 ml of 15% saline

    Step-by-step explanation:

    We can call the amount of 40% solution x and the amount of 15% solution y.

    x + y = 150 -- (1)

    0.40x + 0.15y = 150 * 0.25 -- (2)  --- 150 * 0.25 = 37.5

    40x + 15y = 3750 (Multiply (2) by 100 to get rid of decimals)

    15x + 15y = 2250 -- (3) (Multiply (1) by 15)

    25x = 1500           (Subtract (3) from (1)

    x = 60

    y = 150 - 60 = 90

  2. You eliminate or ‘take away’ the answers that you know or think that r wrong. The last answer that’s left is your answer.

  3. [tex]37.5= 0.4 x +0.15 y[/tex]

    We can solve for x and we got:

    [tex]x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]

    And replacing into the water condition we have:

    [tex]112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]

    Solving for y we got:

    [tex]112.5= 56.25 -0.225 y+0.85 y[/tex]

    [tex]y = \frac{112.5-56.25}{0.625}= 90[/tex]

    And then solving for x we got:

    [tex]x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]

    So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution

    Step-by-step explanation:

    We can solve this problem with the following system of equations:

    [tex]150*0.25 = x*0.4 + y *0.15[/tex] salt

    [tex]150*(1-0.25)= x(1-0.4) +y(1-0.15)[/tex] water

    With x the ml of solution for 40% concentration and y the ml of solution at 15% of concentration

    From the salt condition we have:

    [tex]37.5= 0.4 x +0.15 y[/tex]

    We can solve for x and we got:

    [tex]x= \frac{37.5-0.15y}{0.4}= 93.75-0.375 y[/tex]

    And replacing into the water condition we have:

    [tex]112.5 = (93.75-0.375 y)*0.6 +0.85y[/tex]

    Solving for y we got:

    [tex]112.5= 56.25 -0.225 y+0.85 y[/tex]

    [tex]y = \frac{112.5-56.25}{0.625}= 90[/tex]

    And then solving for x we got:

    [tex]x=\frac{37.5- 0.15*90}{0.4}= 60[/tex]

    So we need 60 ml for the solution of 40% saline and 90 ml for the 15% saline solution

  4. (31)

    let x and y be the 2 numbers, x > y, then

    x + y = 12 and

    x - y = 4

    add the 2 equations term by term

    2x = 16 ( divide both sides by 2 )

    x = 8

    substitute x = 8 into x + y = 12

    8 + y = 12 ⇔ y = 12 - 8 = 4

    the 2 numbers are 8 and 4

    (32)

    let the 2 numbers be x and y, x > y, then

    x - y = 3 and

    x + y = 13

    add the 2 equations term by term

    2x = 16 ( divide both sides by 2 )

    x = 8

    substitute x = 8 into x + y = 13

    8 + y = 13 ⇒ y = 13 - 8 = 5

    the 2 numbers are 8 and 5

    (33)

    let s be the cost of senior citizen ticket and c be the cost of a child ticket, then

    3s + c = 38 → (1)

    3s + 2c = 52 → (2)

    subtract (1) from (2) term by term

    c = 14

    substitute c = 14 into (1)

    3s + 14 = 38 ( subtract 14 from both sides )

    3s = 24 ( divide both sides by 3 )

    s = 8

    the cost of a senior citizen ticket is $8 and a child ticket is $14

  5. x=4, y=1. (4, 1).

    Step-by-step explanation:

    -3x-y=-13

    x+2y=6

    x=6-2y

    -3(6-2y)-y=-13

    -18+6y-y=-13

    -18+5y=-13

    5y=-13-(-18)

    5y=-13+18

    5y=5

    y=5/5

    y=1

    x+2(1)=6

    x+2=6

    x=6-2

    x=4

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