Thanks Dylan! But I wanted to know HOW to WRITE OTHER equations to have the same answers as the ones below? NOT how to solve these!

2x+5y=8
x-3y=-7

I will assume you don't want just multiples of the above, so we will need the actual solution to yours first

double the second:
2x - 6y = -14
subtract form the first
11y = 22
y = 2
then in the second:
x - 6 = -7
x = -1

now just make up any combination of x's and y's, sub in the 2 values and see what constant you get
e.g.
4x + 3y = -4 + 6 = 2
so 4x + 3y = 2 is one equation.
Now do the same thing for a second one

Many thanks Reiny!!

To write other equations that will have the same solutions as the given equations, you can use linear equations that are multiples or linear combinations of the original equations.

First, let's examine the given equations:
1) 2x + 5y = 8
2) x - 3y = -7

To create a new equation with the same solutions, you can multiply one or both of the original equations by a constant. This constant can be any non-zero number. Let's multiply equation (1) by 3 and equation (2) by 2:

3 * (2x + 5y) = 3 * 8
2 * (x - 3y) = 2 * (-7)

This gives us:
3(2x) + 3(5y) = 24
2(x) - 2(3y) = -14

Simplifying these equations, we have:
6x + 15y = 24
2x - 6y = -14

Now we have two new equations that have the same solutions as the original ones.

You can also create other equations by combining the original equations through addition or subtraction. Let's add the two original equations together:

(2x + 5y) + (x - 3y) = 8 + (-7)

This gives us:
3x + 2y = 1

Now we have another equation that will have the same solutions as the original ones.

In summary, to create other equations with the same solutions as the given ones:
- Multiply one or both of the original equations by a constant.
- Combine the original equations by addition or subtraction.

Remember, it's important to ensure that the coefficients of x and y remain the same while manipulating the equations.