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Example Questions
Example Question #31 : Solving Equations
Solve
if .
Plug in
for in the equation to get
Example Question #32 : Solving Equations
Solve for
. When .
Given the equation,
and
Plug in
for to the equation,
Solve and simplify.
Example Question #85 : Functions And Lines
Solve for
, when .
Plug in the
value for .
Simplify
Subtract
Example Question #31 : Solving Equations
If
and
Solve for
and .None of the available answers
rearranges to
and
, so
Example Question #32 : Solving Equations
Solve for
in the system of equations:
The system has no solution
In the second equation, you can substitute
for from the first.
Now, substitute 2 for
in the first equation:
The solution is
Example Question #33 : Solving Equations
Solve for
:
None of the other answers
To solve for
, you must isolate it from the other variables. Start by adding to both sides to give you . Now, you need only to divide from both sides to completely isolate . This gives you a solution of .Example Question #81 : Functions And Lines
For the following equation, if x = 2, what is y?
9
7
25
16
1
9
On the equation, replace x with 2 and then simplify.
Example Question #3 : Equations / Solution Sets
Solve for
.
This is a quadratic equation. We can solve for
either by factoring or using the quadratic formula. Since this equation is factorable, I will present the factoring method here.The factored form of our equation should be in the format
.To yield the first value in our original equation (
), and .
To yield the final term in our original equation (
), we can set and .
Now that the equation has been factored, we can evaluate
. We set each factored term equal to zero and solve.
Example Question #34 : Solving Equations
Without drawing a graph of either equation, find the point where the two lines intersect.
Line 1 :
Line 2 :
To find the point where these two lines intersect, set the equations equal to each other, such that
is substituted with the side of the second equation. Solving this new equation for will give the -coordinate of the point of intersection.
Subtract
from both sides.
Divide both sides by 2.
Now substitute
into either equation to find the -coordinate of the point of intersection.
With both coordinates, we know the point of intersection is
. One can plug in for and for in both equations to verify that this is correct.Example Question #35 : Solving Equations
What is the sum of
and for the following system of equations?
Add the equations together.
Put the terms together to see that .
Substitute this value into one of the original equaitons and solve for
.
Now we know that , thus we can find the sum of
and
.
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