# How do you solve by substitution #3x + 2y = 11# and #x - 2 = -4y#?

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To solve the system of equations by substitution, we first solve one of the equations for one variable and then substitute that expression into the other equation.

In this case, let's solve the second equation, ( x - 2 = -4y ), for ( x ): [ x = -4y + 2 ]

Now, substitute this expression for ( x ) into the first equation: [ 3(-4y + 2) + 2y = 11 ]

Now, solve for ( y ): [ -12y + 6 + 2y = 11 ] [ -10y + 6 = 11 ] [ -10y = 5 ] [ y = -\frac{1}{2} ]

Now that we have found the value of ( y ), substitute it back into one of the original equations to find the value of ( x ). Using the second equation: [ x - 2 = -4(-\frac{1}{2}) ] [ x - 2 = 2 ] [ x = 4 ]

Therefore, the solution to the system of equations is ( x = 4 ) and ( y = -\frac{1}{2} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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