0
Find the solution to the system of equations 3x plus y plus z equals 6 3x - y plus 2z equals 9 y plus z equals 3?
3x + y + z = 6
3x - y + 2z = 9
y + z = 3
y + z = 3
y = 3 - z (substitute 3 - z for y into the first equation of the system)
3x + y + z = 6
3x + (3 - z) + z = 6
3x + 3 = 6
3x = 3
x = 1 (substitute 3 - z for y and 1 for x into the second equation of the system)
3x - y + 2z = 9
3(1) - (3 - z) + 2z = 9
3 - 3 + z + 2z = 9
3z = 9
z = 3 (which yields y = 0)
y = 3 - z = 3 - 3 = 0
So that solution of the system of the equations is x = 1, y = 0, and z = 3.
What else can I help you with?
Can substitution in math be used to find the exact solution of a system of equations?
yes
What are multi step equations?
They are equations that involve many steps to find the solution.
Solve by substitution y equals -4x - 7 and y equals 3x?
The easiest way to solve this system of equations is to solve for a variable in one of the equations. In the second equation, y = 3x. This can be substituted into the first equation: y = -4x - 7; 3x = = -4x - 7; 7x = -7; x = -1. Since we have determined that x equals -1, we can then substitute -1 into either equation to find our corresponding y-value. Thus: y = 3x; y = 3(-1) y = -3. Thus, the solution to this system of equations is (-1, -3).
What does solving a system of equations actually mean?
That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.That means to find values for all the variables involved, so that they satisfy ALL the equations in a system (= set) of equations.
Solving the system of equations by graphing?
Solving a system of equations by graphing involves plotting the equations on the same coordinate plane and finding the point(s) where the graphs intersect, which represents the solution(s) to the system. Each equation corresponds to a line on the graph, and the intersection point(s) are where the x and y values satisfy both equations simultaneously. This method is visually intuitive but may not always provide precise solutions, especially when dealing with non-linear equations or when the intersection point is not easily identifiable due to the scale or nature of the graphs.
What is a solution to the following system of equations using substitution -5x plus y equals -5?
-10
Can substitution in math be used to find the exact solution of a system of equations?
yes
How do you check a solution to a system of equations?
Put the values that you find (as the solution) back into one (or more) of the original equations and evaluate them. If they remain true then the solution checks out. If one equation does not contain all the variables involved in the system, you may have to repeat with another of the original equations.
When solving a system of equations by elimination you find what?
You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.
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.
How do you find the solution to system of equations?
Parenthesis, exponents, multiplication, division, addition, subtraction. PEMDAS
When we look for a solution for a system of equations or inequalities are we looking into an AND situation or an OR situation?
Unless otherwise stated, the "AND" case is normally assumed, i.e., you have to find a solution that satisfies ALL equations.
What is the solution of x plus y equals 5?
You have two unknown variables, x and y. You therefore need at least two independent equations to find a solution.
What is the purpose of Cramer's rule?
In math, the purpose of Cramer's rule is to be able to find the solution of a system of linear equations by using determinants and matrices. Cramer's rule makes it easy to find a system of equations that have many unknown variables.
What are multi step equations?
They are equations that involve many steps to find the solution.
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?
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)
When you formulate a system of equations you have at least how many factors?
You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.
