Maths-

General

Easy

Question

Rewrite the equation as a system of equations, and then use a graph to solve.
$2 x squared plus 3 x equals 2 x plus 1$

hint Hint:

A graph is a geometrical representation of an equation or an expression. It can be used to find solutions of equation.
We are asked to rewrite the equation as system of equations and graph them to solve it.

The correct answer is: We are asked to rewrite the equation as system of equations and graph them to solve it.

Step 1 of 3:
Equate each side of the equation to a new variable, y :
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x squared plus 3 x end cell row cell y equals 2 x plus 1 space space space space end cell end table$
Thus, we get a system of equation.
Step 2 of 2:
Consider the equation, y = 2x2 + 3x. Find three solutions for the equation.
when x = 0,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals 0 space space space space space space space space space space space space space space space space space space end cell row cell y equals 2 left parenthesis 0 right parenthesis plus 3 left parenthesis 0 right parenthesis space space space end cell row cell y equals 0 space space space space space space space space space space space space space space space space space space end cell end table space$
when x = -1,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x squared plus 3 x space space space space space space space space space space space space end cell row cell y equals 2 left parenthesis negative 1 right parenthesis squared plus 3 left parenthesis negative 1 right parenthesis end cell row cell y equals 2 minus 3 space space space space space space space space space space space space space space space space space space space end cell row cell y equals negative 1 space space space space space space space space space space space space space space space space space space space space space space end cell end table$
when x = 1,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x squared plus 3 x space space space space space end cell row cell y equals 2 left parenthesis 1 right parenthesis squared plus 3 left parenthesis 1 right parenthesis end cell row cell y equals 2 plus 3 space space space space space space space space space space space end cell row cell y equals 5 space space space space space space space space space space space space space space space space space end cell end table$
Thus, the points are; (0, 0) )(-1, -1) and (1,5)
Consider the equation y = 2x+y and find two solutions.
when x = 0,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x plus 1 space space end cell row cell y equals 2 left parenthesis 0 right parenthesis plus 1 end cell row cell y equals 1 space space space space space space space space space space space end cell end table$
when x = 1,

Thus, the required points are; (0,1) and (1, 3)
Step 3 of 3:
Plot the points and join them to get the respective graphs.

Here, they graphs intersect at two point; (-1 -1) and (0.5, 2). This means that the solutions of the system of equation are (-1 -1) and (0.5, 2).

Solutions of a set of equation can be found by graphing the equations and finding the intersecting points. The points where they intersect are the solutions.

Rewrite the equation as a system of equations, and then use a graph to solve.
$4 x squared equals 2 x minus 5$

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$y equals x squared plus 6 x plus 9$
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It is not necessary for every set of equation to have solutions. If you graph them and get not intersecting points, then they have no real solutions.

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$y equals x squared plus 6 x plus 9$
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It is not necessary for every set of equation to have solutions. If you graph them and get not intersecting points, then they have no real solutions.

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Rewrite the equation as a system of equations, and then use a graph to solve.

A graph is a geometrical representation of an equation or an expression. It can be used to find solutions of equation.We are asked to rewrite the equation as system of equations and graph them to solve it.

The correct answer is: We are asked to rewrite the equation as system of equations and graph them to solve it.

Related Questions to study

Rewrite the equation as a system of equations, and then use a graph to solve.

Rewrite the equation as a system of equations, and then use a graph to solve.

Find the simple interest on Rs. 8000 at 16 % per annum for 9 months?

Find the simple interest on Rs. 8000 at 16 % per annum for 9 months?

The simple interest on a sum of money at the end of 5 years is of the sum. Find the rate of interest?

The simple interest on a sum of money at the end of 5 years is of the sum. Find the rate of interest?

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If Rs. 4000 amounts to Rs. 4500 in 2 years, find how much would it amount in 5 years at the same rate of interest?

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Rewrite the equation as a system of equations, and then use a graph to solve.
$2 x squared plus 3 x equals 2 x plus 1$

A graph is a geometrical representation of an equation or an expression. It can be used to find solutions of equation.
We are asked to rewrite the equation as system of equations and graph them to solve it.

Rewrite the equation as a system of equations, and then use a graph to solve.
$4 x squared equals 2 x minus 5$

Rewrite the equation as a system of equations, and then use a graph to solve.
$4 x squared equals 2 x minus 5$

Find the solution of the system of equations.
$y equals 2 x squared plus 5 x minus 30$
y = 2x + 5

Find the solution of the system of equations.
$y equals 2 x squared plus 5 x minus 30$
y = 2x + 5

Format the sentence into converts Spanish grammar.
"My wife buys a new television for my father”

Format the sentence into converts Spanish grammar.
"My wife buys a new television for my father”

Find the solution of the system of equations.
$y equals 3 x squared plus 2 x plus 1$
$y equals 2 x plus 1$

Find the solution of the system of equations.
$y equals 3 x squared plus 2 x plus 1$
$y equals 2 x plus 1$

Find the solution of the system of equations.
$y equals x squared plus 8 x plus 30$
y = 5 - 2x

Find the solution of the system of equations.
$y equals x squared plus 8 x plus 30$
y = 5 - 2x

Find the solution of the system of equations.
$y equals x squared plus 6 x plus 9$
y = 3x

Find the solution of the system of equations.
$y equals x squared plus 6 x plus 9$
y = 3x

Find the solution of the system of equations.
$y equals x squared minus 5 x minus 8$
$y equals negative 2 x minus 4$

Find the solution of the system of equations.
$y equals x squared minus 5 x minus 8$
$y equals negative 2 x minus 4$