Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
8x + 11y = -50
-32x – 44y = -200
multiply first equation by 4
+32 x + 44 y = -200
-32 x - 44 y = -200
multiply second equation by -1
+32 x + 44 y = -200
+32 x + 44 y = +200
These are two parallel lines. They never intersect. There is no solution.
i'm lost
Well, say x + y = 1
and x + y = 2
that is impossible. There is no single point where x+y = two different numbers.
If you graph those two lines, you will see that they are parallel to each other and never cross.
To solve the system of equations using the elimination method, the goal is to eliminate one of the variables by adding or subtracting the equations. We will start by multiplying the first equation by 4 to make the coefficients of x in both equations opposites.
Original equations:
Equation 1: 8x + 11y = -50
Equation 2: -32x - 44y = -200
Now, we will multiply Equation 1 by 4:
4(8x + 11y) = 4(-50)
32x + 44y = -200
Now, the two equations are:
Equation 1: 32x + 44y = -200
Equation 2: -32x - 44y = -200
Next, we will add the two equations together to eliminate the x variable:
(32x + 44y) + (-32x - 44y) = -200 + (-200)
32x - 32x + 44y - 44y = -400
0 = -400
We are left with 0 = -400, which is always false. This means that the system of equations has no solution. There is no value of x and y that simultaneously satisfy both equations.
Therefore, the system of equations has no solution.