Can someone teach me how to solve this equation using substitution or elimination for

{-3x+2y=23
{5x+2y=-17

notice the 2y terms, that suggests if you subtract one equation from another, you eliminate the y term.

Subtract the second from the first.
5x-(-3x)+2y-2y=23-(-17)
8x+0y=40
x=5
now put that into either equation, and solve for y
-3(5)+2y=23
2y=23+15
y=24

eq. 1 says 2y = 3x+23

use that in eq. 2 and you have

5x + 3x+23 = -17

for elimination, this web site gives all the details:

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

Sure! I can explain how to solve this system of equations using substitution and elimination.

Let's start by explaining the method of substitution.
1. Solve one of the equations for one variable in terms of the other.
In this case, let's solve the first equation for x in terms of y.
-3x + 2y = 23
To isolate x, we can add 3x to both sides:
2y = 3x + 23
Now, divide both sides by 3 to solve for x:
x = (2y + 23)/3

2. Substitute the expression we found for x into the other equation.
Now, substitute the expression (2y + 23)/3 for x in the second equation:
5x + 2y = -17
5((2y + 23)/3) + 2y = -17

3. Simplify and solve for y.
To solve for y, we need to simplify the equation and isolate y.
Multiply both sides by 3 to get rid of the fraction:
5(2y + 23) + 6y = -51
10y + 115 + 6y = -51
Combine like terms:
16y + 115 = -51
Subtract 115 from both sides:
16y = -51 - 115
16y = -166
Divide both sides by 16:
y = -166/16
Simplify the fraction:
y = -10.375

4. Substitute the value of y into one of the original equations to solve for x.
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
-3x + 2y = 23
-3x + 2(-10.375) = 23
Simplify:
-3x - 20.75 = 23
Add 20.75 to both sides:
-3x = 43.75
Divide both sides by -3:
x = -43.75/3
Simplify the fraction:
x ≈ -14.6

So, the solution to the system of equations is x ≈ -14.6 and y ≈ -10.375.

Now, let's explain the method of elimination briefly.
1. Multiply both sides of one of the equations by a constant so that the coefficients of one of the variables are equal in both equations.
In this case, let's multiply the first equation by 5 to make the coefficients of x the same.
-3x + 2y = 23 (Original 1st equation)
5(-3x + 2y) = 5(23)
-15x + 10y = 115

2. Add or subtract the equations to eliminate one of the variables.
Now, subtract the second equation from the modified first equation:
(-15x + 10y) - (5x + 2y) = 115 - (-17)
-15x + 10y - 5x - 2y = 115 + 17
-20x + 8y = 132

3. Solve for one variable.
Now, we can choose either x or y to solve for. In this case, let's solve for y. We need to isolate y.
-20x + 8y = 132
Rearrange the equation:
8y = 20x + 132
Divide both sides by 8:
y = (20x + 132)/8
Simplify the fraction:
y = 5x + 16.5

4. Substitute the value of y into one of the original equations to solve for x.
Now, substitute the expression 5x + 16.5 for y in the first equation:
-3x + 2(5x + 16.5) = 23
-3x + 10x + 33 = 23
Combine like terms:
7x + 33 = 23
Subtract 33 from both sides:
7x = 23 - 33
7x = -10
Divide both sides by 7:
x = -10/7
Simplify the fraction:
x ≈ -1.43

So, the solution to the system of equations using the elimination method is x ≈ -1.43 and y ≈ 5(-1.43) + 16.5 ≈ 8.79.

Both substitution and elimination methods yield the same solution for the given system of equations.