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Solve by using system of equations and substatuion

-3x - y = -13

x + 2y = 6

*Show work!

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

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♡

Solve by using system of equations and substatuion

-3x - y = -13

x + 2y = 6

*Show work!

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

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

[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

(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

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