Solve the following system: 2x-6y = 26 3x+5y = -3

from the first:

2x-6y=26 --> x = 3y + 13

sub into the 2nd and away you go ....

To solve the given system of equations:

Step 1: Choose one of the equations and isolate one variable in terms of the other. Let's solve the second equation for x:
3x + 5y = -3
3x = -3 - 5y
3x = -3 - 5y
x = (-3 - 5y)/3

Step 2: Substitute the value of x from the previous step into the other equation:
2x - 6y = 26
2[(-3 - 5y)/3] - 6y = 26

Step 3: Simplify the equation:
(-6 - 10y)/3 - 6y = 26

Step 4: Multiply through by 3 to eliminate the denominator:
-6 - 10y - 18y = 78

Step 5: Combine like terms:
-6 - 28y = 78

Step 6: Move the constant term to the other side of the equation:
-6 = 78 + 28y

Step 7: Simplify further:
-6 = 28y + 78

Step 8: Move the variable term to the other side of the equation:
-6 -78 = 28y

Step 9: Simplify:
-84 = 28y

Step 10: Divide through by 28 to solve for y:
y = -84/28
y = -3

Step 11: Substitute the value of y back into one of the original equations to find x. Let's substitute it into the first equation:
2x - 6(-3) = 26
2x + 18 = 26

Step 12: Simplify:
2x = 26 - 18
2x = 8

Step 13: Divide through by 2 to solve for x:
x = 8/2
x = 4

Therefore, the solution to the given system of equations is x = 4 and y = -3.