Answer: The ordered pair is (2,3)
Step-by-step explanation:
To solve this problem, we can use substitution. With substitution, we substitute the y in each problem with the equations. In this case, x + 1 can substitute the y in y = -x + 5. Here is what the problem looks like now:
x + 1 = -x + 5
The reason we used substitution is because we assume that these linear equations are equal. We must prove it, though. We can use algebra.
Move the variables to one side and the numerical values to another:
x + x = 5 - 1.
Simplify.
2x = 4
Simplify.
x = 2.
Now, we got our x value, we can substitute it into our problem:
y = 2 + 1
y + -2 + 5
2 + 1 = - 2 + 5 = 3
Our x is 2, and our y is 3. The ordered pair that is a solution is (2,3).
The required answer is yes and the odered pair is [tex](2,3)[/tex].
Given:
The given linear equations are:
[tex]y=x+1[/tex]
[tex]y=-x+5[/tex]
To find:
Whether the given linear equations has an ordered pair that is a solution to both of the given linear equations.
Explanation:
The slope-intercept form of a linear equation is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
On comparing the given equation with the slope intercept form, we get [tex]m_1=1[/tex] and [tex]m_2=-1[/tex].
The slopes of the given lines are different, therefore the lines are not parallel and they have an ordered pair that is a solution to both of the given linear equations.
Adding both equations, we get
[tex]2y=6[/tex]
[tex]y=\dfrac{6}{2}[/tex]
[tex]y=3[/tex]
Substituting this value in the first equation, we get
[tex]3=x+1[/tex]
[tex]3-1=x[/tex]
[tex]2=x[/tex]
Therefore, the required answer is yes and the odered pair is [tex](2,3)[/tex].
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