Maths-

General

Easy

Question

Find the solution of the system of equations.
$y equals 0.5 x squared minus 8 x plus 13$
$y equals x minus 3$

hint Hint:

A quadratic equation of the form $x squared plus open parentheses a plus b close parentheses x plus a b$ can be simplified into $open parentheses x plus a right parenthesis left parenthesis x plus b close parentheses$ . This can be further solved by equating it to zero.
We are asked to solve the set of equation.

The correct answer is: We are asked to solve the set of equation.

Step 1 of 3:
The LHS of the given set is same. Hence, equate the equations.
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 0.5 x squared minus 8 x plus 13 equals x minus 3 space space space space space space end cell row cell 0.5 x squared minus 8 x minus x plus 13 plus 3 equals 0 end cell row cell 0.5 x squared minus 9 x plus 16 equals 0 space space space space space space space space space space space space end cell row cell 5 x squared minus 90 x plus 160 equals 0 space space space space space space space space space space space end cell row cell x squared minus 18 x plus 32 equals 0 space space space space space space space space space space space space space space end cell end table space$
Here, we multiply the whole equation by ten to remove the decimal. After then, we take out the five to simplify them.
Step 2 of 3:
Solve the simplified equation:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared minus 18 x plus 32 equals 0 space space space space space space space space space space space end cell row cell x squared minus 16 x minus 2 x plus 32 equals 0 space space space end cell row cell x left parenthesis x minus 16 right parenthesis minus 2 left parenthesis x minus 16 right parenthesis equals 0 end cell row cell left parenthesis x minus 2 right parenthesis left parenthesis x minus 16 right parenthesis equals 0 space space space space space space space space space space space end cell row cell left parenthesis x minus 2 right parenthesis equals 0 straight & left parenthesis x minus 16 right parenthesis equals 0 space space end cell row cell x equals 2 straight & x equals 16 space space space space space space space space space space space space space space space space space end cell end table$
Step 3 of 3:
Substitute the found values of x in any of the equations to get the values of y;
When x=2,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals x minus 3 end cell row cell y equals 2 minus 3 end cell row cell y equals negative 1 end cell end table$
When x=16,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals x minus 3 space space end cell row cell y equals 16 minus 3 end cell row cell y equals 13 space space space space space space end cell end table$
Thus, the required solutions are: (2, -1) and (16, 13)

You can also solve a set of equation by graphing them. The points where the equations intersect all together would be their solutions.

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Find the solution of the system of equations.

A quadratic equation of the form can be simplified into . This can be further solved by equating it to zero.We are asked to solve the set of equation.

The correct answer is: We are asked to solve the set of equation.

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Find the solution of the system of equations.
$y equals 0.5 x squared minus 8 x plus 13$
$y equals x minus 3$

Find the solution of the system of equations.
$y equals negative 4 x squared plus x plus 1$
$y equals negative 7 x plus 1$

Find the solution of the system of equations.
$y equals negative 4 x squared plus x plus 1$
$y equals negative 7 x plus 1$

Find the solution of the system of equations.
$y equals x squared plus 3 x minus 2$
Y= 2x

Find the solution of the system of equations.
$y equals x squared plus 3 x minus 2$
Y= 2x

Given the equation $y equals x squared plus 3 x plus 2$ , write an equation for a line that does not intersect the parabola.

Given the equation $y equals x squared plus 3 x plus 2$ , write an equation for a line that does not intersect the parabola.

Given the equation $y equals x squared plus 3 x plus 2$ , write an equation for a line that intersects the parabola two times.

Given the equation $y equals x squared plus 3 x plus 2$ , write an equation for a line that intersects the parabola two times.

Complete the sentence with the best prefix
Let's re start the game after a short break

Complete the sentence with the best prefix
Let's re start the game after a short break