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.
Chat with our AI personalities
yes
They are equations that involve many steps to find the solution.
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).
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 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.