-3x + 2y = 11
3x - 4y = -19
add the equatons
-2y=-8
y=4
3x-4(4)=-19
3x=-3
x=-1
-3x + 2y = +11
+3x - 4y = -19
--------------- add
0 -2 y = -8
y = 4
then
-3 x + 8 = 11
3x= -3
x = -1
To find the solution to this system of equations, you can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the two equations. Let's start by eliminating the variable x:
-3x + 2y = 11 (Equation 1)
3x - 4y = -19 (Equation 2)
To eliminate x, we can add Equation 1 and Equation 2 together:
(-3x + 2y) + (3x - 4y) = 11 + (-19)
-3x + 3x + 2y - 4y = -8
-2y = -8
Now, we have the equation -2y = -8. We can solve this equation by dividing both sides by -2:
(-2y)/(-2) = (-8)/(-2)
y = 4
So we have found that y = 4. Now, we can substitute this value back into one of the original equations to solve for x. Let's use Equation 1:
-3x + 2y = 11
Substituting y = 4:
-3x + 2(4) = 11
-3x + 8 = 11
Now, we can solve for x. Subtract 8 from both sides:
-3x = 3
Divide both sides by -3:
x = -1
So the solution to the system of equations is x = -1 and y = 4.