How do you solve #2x+5y=11# and #4x+3y=1# using substitution?
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 Solve the first equation for x or y.
 Substitute the expression from step 1 into the other equation.
 Solve the resulting equation for the variable.
 Substitute the value found in step 3 back into the equation from step 1 to find the other variable.
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To solve the system of equations (2x + 5y = 11) and (4x + 3y = 1) using substitution:
 Solve one of the equations for one variable in terms of the other.
 Substitute the expression found in step 1 into the other equation.
 Solve the resulting equation for the remaining variable.
 Substitute the value found in step 3 into either of the original equations to solve for the other variable.
 Verify the solution by checking it in both original equations.
Stepbystep:

Solve the first equation (2x + 5y = 11) for (x): [2x = 11  5y] [x = \frac{11}{2}  \frac{5}{2}y]

Substitute (x = \frac{11}{2}  \frac{5}{2}y) into the second equation (4x + 3y = 1): [4\left(\frac{11}{2}  \frac{5}{2}y\right) + 3y = 1]

Solve for (y): [22  10y + 3y = 1] [22  7y = 1] [7y = 1  22] [7y = 21] [y = 3]

Substitute (y = 3) into (x = \frac{11}{2}  \frac{5}{2}y): [x = \frac{11}{2}  \frac{5}{2}(3)] [x = \frac{11}{2}  \frac{15}{2}] [x = 2]

Verify the solution by checking it in both original equations: [2(2) + 5(3) = 11] [4(2) + 3(3) = 1]
Both equations are satisfied by (x = 2) and (y = 3), so the solution is correct.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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