3x + 8y = -5
-2x + 2y = 18
Multiply the 2nd equation by -4 so the y's will eliminate when you add the two equations together.
3x + 8y = - 5
8x -8y = -72
11x = -77 x = -7
find y by substituting into one of the original equations.
To solve the system of equations:
1. Start by choosing one of the equations and solve for one variable in terms of the other.
Let's solve the second equation for x:
-2x + 2y = 18
Add 2x to both sides of the equation:
-2x + 2x + 2y = 18 + 2x
Simplify:
2y = 2x + 18
Divide both sides of the equation by 2:
y = (2x + 18)/2
y = x + 9
2. Next, substitute the value we found for y back into the first equation.
3x + 8y = -5
Replace y with x + 9:
3x + 8(x + 9) = -5
Distribute the 8:
3x + 8x + 72 = -5
Add like terms:
11x + 72 = -5
Subtract 72 from both sides of the equation:
11x = -5 - 72
Simplify:
11x = -77
Divide both sides of the equation by 11:
x = -77/11
x = -7
3. Finally, substitute the value we found for x back into the second equation to solve for y:
-2x + 2y = 18
Replace x with -7:
-2(-7) + 2y = 18
Simplify:
14 + 2y = 18
Subtract 14 from both sides of the equation:
2y = 18 - 14
Simplify:
2y = 4
Divide both sides of the equation by 2:
y = 4/2
y = 2
So the solution to the system of equations is x = -7 and y = 2.