Question
Which of the following could be the x-coordinate of a solution to the system of equations above?
Hint:
Hint:
To find the x co-ordinate, we first need to find the solution of the given system of equations. To solve these equations, we simply need to put the value of y from the second equation in the first equation. We get an equation in one variable x. This can be easily solved to get the value of the x coordinate which is x.
The correct answer is:
The given equations are
Putting the value of from the second equation in the first, we get
Applying the formula
We get,
Applying the formula again, we have
Simplifying the above equation, we get
We add the co-efficient of terms which have the same degree of x.
Bringing all the terms to the left hand side and solving for x, we get
Dividing by 5 on both sides, we have
Taking the positive square root both sides, we get
Note:
If we had to find the y-coordinate of the system of equations, then we put this value of x in the equation 
to get the value of y. Here, we got a quadratic equation of x, which did not have any term containing x, so it was easier to solve. If the quadratic equation was of the form 
, then we would use the quadratic formula 
to solve the equation.
Related Questions to study
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Solve the equation and check your result 6(3m + 2) – 2(6m – 1) = 3(m – 8) – 6(7m – 6) +9m
Solve and check your answer: 3x – 2(2x – 5) = 2(x + 3) – 8
Solve and check your answer: 3x – 2(2x – 5) = 2(x + 3) – 8
Solve: 16 = 4 + 3(x + 2)
Solve: 16 = 4 + 3(x + 2)
The graph of the function f is shown in the xy-plane above, where y =f 
. Which of the following functions could define f ?
Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.
The graph of the function f is shown in the xy-plane above, where y =f . Which of the following functions could define f ?
Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?
f(x) =2x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?
f(x) =2x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of y= d(t) on the right could represent which of the following as a function of time from when the wheel began to roll?
Which of the following is equivalent to 
?
Which of the following is equivalent to ?
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.
If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x
In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?
Note:
As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x
