Sovle using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this
-2x + 3y = -37.5
-4x + 0y = -24
Why would you state "0y" which = 0?
Multiply first equation by 2.
-4x + 6y = -75
-4x +0y = -24
Subtract equation 2 from equation 1.
6x = -51
Find x and insert value to get y.
To solve this system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations by a constant, so that when we add or subtract the equations, one of the variables cancels out.
In this case, we can see that the second equation already has a coefficient of 0 for y, which means we don't need to do anything to eliminate the y variable. We can start by adding the two equations together:
(-2x + 3y) + (-4x + 0y) = -37.5 + (-24)
Simplifying the equation, we get:
-2x + 3y - 4x = -37.5 - 24
Combining like terms, we have:
-6x + 3y = -61.5
Now we have a new equation that relates x and y. Let's rearrange it to isolate one of the variables:
-6x = -3y - 61.5
Next, we can solve for x by dividing both sides of the equation by -6:
x = (-3y - 61.5) / -6
Simplifying further, we have:
x = (3y + 61.5) / 6
Now we have an equation expressing x in terms of y. However, since we don't have a specific value for y, we can say that the system has infinitely many solutions. Each value of y will correspond to a unique solution for x.