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Which graph could be used to find the solution of the system of equations y equals 2x plus 6 and y equals x2 plus 4x plus 3?
Wiki User
∙ 12y ago
One way would be to graph the two equations: the parabola y = x² + 4x + 3, and the straight line y = 2x + 6. The two points where the straight line intersects the parabola are the solutions.
The 2 solution points are (1,8) and (-3,0)
Wiki User
∙ 12y ago
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How many solutions does a system of equations have?
It depends on the equation. It could have one, it could have an infinite number.
When the equation in a linear system have different slopes then the system has what kind of solution?
It is not possible to tell. The lines could intersect, in pairs, at several different points giving no solution. A much less likely outcome is that they all intersect at a single point: the unique solution to the system.
In order to solve the following system of equations by addition which could you do before adding the equations so that one variable will be eliminated when you add them?
Multiply the top equation by -3 and the bottom equation by 2.
What does it mean to find the solutions of system of inequalities?
In 2-dimensional space, an equality could be represented by a line. A set of equalities would be represented by a set of lines. If these lines intersected at a single point, that point would be the solution to the set of equations. With inequalities, instead of a line you get a region - one side of the line representing the corresponding equality (or the other). The line, itself, may be included or excluded. Each inequality can be represented by a region and, if these regions overlap, any point within that sub-region is a solution to the system of inequalities.
What does an exclamation mark mean in equations?
lets say the equation says 5! that means 5x4x3x2x1 which equals 120 it is call five factorial based on what number is put in front of it it could be six factorial, seven factorial, etc..
Does the solution to a system of three equations in three variables is always one point?
No. There could be no solution - no values for x, y, and z so that the 3 equations are true.
What graph could be used to find the solution of the system of equations y equals 2x plus 6 and y equals x2 plus 4x plus 3?
A graph that has 1 parabolla that has a minimum and 1 positive line.
What are equations with same solution called?
There is no special name. Two totally unrelated equations could have the same solution(s).
How could you show that two equations aren't equivalent?
One way would be to solve the two equations. If they have exactly the same solution set, they are equivalent. Otherwise they are not.
How many solutions does a system of equations have?
It depends on the equation. It could have one, it could have an infinite number.
What clues could help determine between equations and expressions?
An equation has the 'equals' sign ( = ) in it. An expression hasn't.
Why do some systems of equations have one solution?
If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.
Could variables other than x and y be used in a system of equations?
Yes
What it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
Solve this system of equations using the addition methodx plus y equals 3?
Answer by Hilmarz for a very similar question: When talking about a "system of equations", you would normally expect to have two or more equations. It is quite common to have as many equations as you have variables, so in this case you should have two equations. Pricen2: given that there is no second equation with which to solve the original equation the values of x and y could be any of great number of values. If you knew the value of x then you would use y=3-x to find the value of y If you knew the vlaue of y then you would use x=3-y to find the value of x
The solution to an equation is n -5 the equation has parentheses on at least one side of the equation and has variables on both sides of the equation what could the equation be?
n-5 is an expression, it cannot be a solution. Furthermore, there are infinitely many possible equations for which n = 5 could be a solution - even with the added requirements of the question.
How do you solve 6x-3y equals -3 and 8x-4y equals -4 using the linear combination method?
Set up your equations as an addition, lining up like variables:6x - 3y = -38x - 4y = -4First we want to eliminate one of the variables. We do this by getting the scalar multiples for one of the variables to match in both equations.In this example, we can do this by simplifying both equations:Divide the top equation by 3, divide the bottom equation by 4:6/3x - 3/3y = -3/38/4x - 4/4y = -4/4~2x - y = -12x - y = -1Right now, you can already guess that something is wrong, but we will forge on ahead anyways:In order to get one of the variables eliminated, we have to multiply one of the equations by -1, or we can just simply subtract the equations instead of adding them:2x - y = -1+ -2x +y = 1)------------------0x +0y = 0Huh. Isn't that strange - when we eliminated one of the variables, we also eliminated the other variable. What we are left with is 0=0.What this means is that the two equations are linearly dependent, and they in fact overlap each other.HOWEVER, because we are left with 0=0, the system of equations is consistent, so there IS a solution, albeit the solution will be infinite.NOTE: if we had instead been left with a contradiction, such as 0 = 1, or 0=-1 or 0=4, we would say that the system is inconsistent and there is no solution. If you want to be technical, you would say that the solution is the empty set, which you can denote with ø or {}.Since the two lines overlap each other completely, there is in fact only one line in the system. Simply pick one of the equations and simplify. As we already showed above, both equations simplify to the same linear equation:2x - y = -1We may want to isolate one of the variables:2x = -1 + y~2x + 1 = ySo our solution is the line:y = 2x + 1Where x is free.You could also pick y to be your free variable, and write the solution as:x = -1/2 + 1/2y
