How to Determine if (X, Y) is a Solution to a System of Equations
A system of equations is a set of multiple equations with the same variables. To determine whether a given ordered pair \((X, Y)\) is a solution to a system of equations, you need to substitute the values of \(X\) and \(Y\) into each of the equations and check if the equations are satisfied. If they are, then the ordered pair is a solution; if they are not, then it is not a solution.
A Step-by-step determining whether (X, Y) is a Solution to a System of Equations
Here is a step-by-step guide on how to do this:
Step 1: Identify the system of equations
First, you need to have a system of equations. It might look something like this:
Equation 1: \(2x+3y=7\)
Equation 2: \(4x-y=5\)
Step 2: Identify the ordered pair (X, Y)
Next, you will be given an ordered pair, or you may be asked to determine if a particular pair is a solution. The ordered pair will look something like this: \((X, Y) = (1, 2)\).
Step 3: Substitute the ordered pair into the equations
Now you need to substitute the \(X\) and \(Y\) values from the ordered pair into the equations from step 1. The \(X\) value is substituted for \(x\), and the \(Y\) value is substituted for \(y\).
For our example, this would look like this:
For Equation 1: \(2(1)+3(2)=7⇒ 2+6=7\), which is not true.
For Equation 2: \(4(1)-2=5⇒ 4-2=5\), which is also not true.
Step 4: Check if the equations are true
As you can see, neither equation is true when you substitute the given values of \(X\) and \(Y\) into them. This means that the ordered pair \((1, 2)\) is not a solution to this system of equations.
If both equations were true after the substitution, then the ordered pair would be a solution to the system of equations.
In summary, to find out if an ordered pair is a solution to a system of equations, you substitute the \(X\) and \(Y\) values into each equation in the system. If all equations are satisfied, then the ordered pair is a solution; if not, it is not a solution.
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