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1. It can have a unique solution. On a graph this would be single point of intersection.
2. It can no no solutions such as two parallel lines on a graph.
3. It can have an infinite number of solutions such as two equations that represent the same line on a graph.
You can make up examples to see this very easily.
For number 3, take any linear equation such as y=x+1
Now multiply both sides of the equation by 10 10y=10x+10. The solution to the system of those two equations is all real numbers, an infinite solution.
Now for number 2, take any line and just find a parallel line. Easy to do by simply making sure it has the same sloe but a different y intercept.
For the last one, take two lines that intersect. This will most often be the case if you randomly pick two linear equation. Say y =x+1 and y=3x+13. Different slope and different y intercept.
What else can I help you with?
What could be the equation of a parabola with a vertex at -2 1?
There are infinitely many such parabolas, four possibilities are: y = x² - 3 y = 5 - x² x = y² - 3 x = -1 - y² Given the focus as well would give an exact equation
If the ordered pair (3-2) satisfies one of the two linear equations in a system how can you tell whether the point satisfies the other equation of the system?
Substitute the values for the two variables in the second equation. If the resulting equation is true then the point satisfies the second equation and if not, it does not.
Is (4 -3) a solution of this system 3x - 3y 21 5x plus 4y 24?
To determine if (4, -3) is a solution to the system, we need to substitute x = 4 and y = -3 into both equations. For the first equation (3x - 3y = 21): (3(4) - 3(-3) = 12 + 9 = 21) (True) For the second equation (5x + 4y = 24): (5(4) + 4(-3) = 20 - 12 = 8) (False) Since (4, -3) does not satisfy the second equation, it is not a solution to the system.
How do you determine which region to shade to indicate the solution set of a system linear equation?
3
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 is the solution of the system of equation graphed y equals -2 plus 5 y equals x-5?
To find the solution of the system of equations ( y = -2 + 5 ) and ( y = x - 5 ), we first simplify the first equation to ( y = 3 ). Next, we set ( 3 = x - 5 ) from the second equation and solve for ( x ), yielding ( x = 8 ). Therefore, the solution to the system is the point ( (8, 3) ).
WHAT IS The sum of two numbers is 27 and their difference is 3.what system of linear equation satisfies the given condition?
The two numbers are... 12 & 15. The equation is... x equals y times 3
One equation in a system of linear equations has a slope of -3 the other equation has a slope of 4 how many solutions does the system have?
A system of linear equations with slopes of -3 and 4 represents two lines that are not parallel. Since the lines have different slopes, they will intersect at exactly one point. Therefore, the system has one unique solution.
What is the equation of the parabola with a vertex at -1-3?
2
How do you use the numbers 1 - 9 to make a true equation equalling 15?
One of many possibilities is 1 + 2 + 5 + 6 + 7 + 9 - 3 - 4 - 8 = 15
Which equation has a solution of n equals -1?
There are infinitely many possibilities. One of these is n+1 = 0
How many different 3-digit numbers can you make with the digits 1 2 and 3 if repetition is permitted?
27 The first digit can be 1, 2 or 3 for 3 total possibilities. For each of those 3 possibilities, the second digit can be 1, 2 or 3, so that's 3 * 3 = 9 possibilities for the first two digits. For each of those 9 possibilities, the third digit can be 1, 2 or 3, so that's 9 * 3 = 27 possibilities for the three digits.
