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solves 2x +3y=40, 5x +2y=34

You have three options

1) re-arrange them into y=mx + b format, then graph them and see where they cross
or
2) re-arrange to get 1x or 1y alone in one equation and "sub" into the other equation. This is by the substitution method
or
3) Use the elimination method.
In that method you multiply one or both equations by a number so that when you add them up (or subtract them) one of the variables would be eliminated.
In this case... suppose you want to eliminate the x's
If we multiply the first equation by -5, and the second equation by 2 we obtain
-5(2x +3y) = -5(40) that is -10x - 15y = -200
while
2(5x +2y) = 2(34) gives 10x + 4y = 68
When you add these up you obtain...
- 11y = -132
divide both sides by -11
and you have y = 12
now sub that back into one of the originals and solve for x : )

I wont subsitision method

To solve the system of equations 2x + 3y = 40 and 5x + 2y = 34, we can use the method of substitution or the method of elimination. I will explain how to solve it using the method of substitution.

1. Solve one equation for one variable in terms of the other.
Let's solve the first equation, 2x + 3y = 40, for x in terms of y.
2x = 40 - 3y
Divide both sides by 2.
x = (40 - 3y) / 2 --> Equation (1)

2. Substitute the expression we found for x in the second equation.
Replace x in the equation 5x + 2y = 34 with (40 - 3y) / 2.
5((40 - 3y) / 2) + 2y = 34

3. Simplify the equation and solve for y.
Multiply through by 2 to eliminate the fraction.
5(40 - 3y) + 4y = 68
Distribute 5 to the terms inside the parentheses.
200 - 15y + 4y = 68
Combine the y terms and constants.
-11y = 68 - 200
-11y = -132
Divide both sides by -11.
y = (-132) / (-11)
y = 12

4. Substitute the value of y back into Equation (1) to find x.
x = (40 - 3(12)) / 2
x = (40 - 36) / 2
x = 4 / 2
x = 2

Thus, the solution to the system of equations is x = 2 and y = 12.

Eq1: 2x + 3y = 40

Eq2: 5x + 2y = 34
Multiply Eq1 by 2 and Eq2 by 3.
Then subtract Eq2 from Eq1:
4x + 6y = 80
15x + 6y = 102
Diff. -11x = -22
X = 2.
In Eq1, replace x with 2 and solve for y:
2*2 + 3y = 40
Y = 12.

I don't understand

I DONT UNDERSTAND IT