Plug your ordered pair into both of your equations to see if you get they work.
That would be the "solution" to the set of equations.
That would depend on the given system of linear equations which have not been given in the question
an ordered pair that makes both equations true
x = -3/5 and y = -24/5
Tell whether the ordered pair (5, -5) is a solution of the system
That of course will depend on what system of equations are they which have not been given
Do you mean: 4x+7y = 47 and 5x-4y = -5 Then the solutions to the simultaneous equations are: x = 3 and y = 5
Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.
The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.
That means there is no solution.There is no set of numbers that you can assign to the variables in the system of equationsthat will make '2' equal to '0'.
x = y = 3
The system is inconsistent because there is no solution, i.e., no ordered pair, that satisfies both equations. You can see that this will be the case by seeing that their graphs have the same slope (2) but different y-intercepts (2 and 3/4 respectively). So the lines are parallel and will not intersect.
x = 1 and y = 2
It is used for solving a system of linear equations where the number of equations equals the number of variables - and it is known that there is a unique solution.
Check your text book for how to solve it.
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.