Question

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this 14x + 18y = -54 -4x – 14y = 42

Answer 1

We have
\[ 14x+18y=-54\]
\[-4x-14y=42\]
We have to use elimination method,
Let's notice the coefficients of x and y in both the equations. Let's try to eliminate x
Let's multiply first equation by 4 and second by 14 and add both , this will eliminate x
Multiply first by 4, we get
\[56x+72y=-216\]
multiply second by 14 we get
\[-56x-196y=588\]
now let's add the two
\[56x+72y-56x-196y=-216+588\]
now we get
\[\cancel{56x}+72y-\cancel{56x}-196y=-216+588\]
we get
\[-124y=372\]
divide both sides by 124, we get
\[-y=3\]
so we get
\[y=-3\]
now let's substitute y=-3 in any of the equations to find x, say first
\[ 14x+18y=-54\]
y=-3
\[14x+18(-3)=-54\]
we get
\[14x-54=-54\]
add both sides by 54
\[14x=0\]

we get
x=0
and
y=-3

Answer 2

canjura did you understand?

Answer 3

Yes Thank you so much

Answer 4

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