y=-3x+8 y=-5x-2

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kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

Posted on

We can use the substitution method to solve for the solution of the given equations.

if we substitute `y=-3x+8` to the equation `y=-5x-2` , we get

`y=-5x-2`

`(-3x+8)=-5x-2`

`-3x+5x=-2-8`

`2x=-10`

`x=-5`

Then if we substitute the value of x in either of the two equation. Let's say at `y=-3x+8` . We obtain

`y=-3(-5)+8`

`y=15+8`

`y=23`

In other words, the point `(-5,23)` is a solution or intersection of the graphs of the two functions.

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The set of equations made up of y=-3x+8 and y=-5x-2 has to be solved for x and y.

Equate the expression for y from the 2 equations.

y = -3x + 8 = y = -5x - 2

-3x + 8 = -5x - 2

-3x + 5x + 8 - 8 = -5x + 5x - 2 - 8

2x = -10

x = -5

y = -3*x + 8 = -3*-5 + 8 = 15 + 8 = 23

The solution of the given set is x = -5 and y = 23

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

y = -3x + 8   -----(i)

y = -5x - 2    -----(ii)

We can solve the above simultaneous equations with the help of substitution method,

y = -3x + 8

Input this value in equation (ii)

y = -5x - 2 

-3x + 8 = -5x - 2 

-3x + 8 - 8 = -5x - 2 - 8         Subtract 8 from both sides

-3x = -5x - 10 

-3x + 5x = -5x - 10 + 5x        Add 5x to both sides

2x = -10  

2x/2 = -10/2                          Divide both sides by 2

x = -5 

Now input this value in equation (i) to find the value of y,

y = -3x + 8  

y = -3(-5) + 8

y = 15 + 8

y = 23 

You can check the answer by inserting both values in any equation, if they balance on both sides the answer is correct.

 
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kevin0001 | Student, Grade 9 | (Level 1) Salutatorian

Posted on

The given equation is : y = -3x + 8   y = -5x - 2.

1. Look at the equation. Since both equations have = y to them, that means we have to find out what x is. Both of the equation's answer should be equal to each other.

2. Combine.  -3x + 8 = -5x - 2

3. Get the x and numbers on different sides. To do this add 3x and 2 to each side. This is to cancel out one number on one side and add / subtract it to the other side.      10 = -2x          3x cancelled out the -3x and was added to -5x. 2 cancelled the - 2 and was added to 8.

4. Get -2x to be only x. To get -2x to be x simply divide it by -2. Remember that you have to do this to both sides. So 10 is divided by -2 too.

5. Divide

6. Your answer should be x = -5.

7. Check your answers. Replace x in the original equations with -5.

     -3x ( -5 ) + 8 = 23             -5 ( -5 ) - 2 = 23

That means that the answer is correct!

aruv's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

y=-3x+8             (i)

y=-5x-2                (ii)

From (i) and (ii),

L.H.S. of (i) = L.H.S. of (ii)

So

-3x+8=-5x-2

-3x+8+5x=5x-5x-2

2x+8=-2

2x+8-8=-2-8

2x=-10

(2x)/2=(-10)/2

x=-5                         (iii)

Substitute x from (iii) in (i),

y=-3(-5)+8

y=15+8

y=23

Thus

x=-5 and y=23

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