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.

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

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.

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!

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