Certainly! Let's solve the system of equations step-by-step to find the intersection point of the two lines.
We have the equations:
1. [tex]\( y = 2x - 3 \)[/tex]
2. [tex]\( y = -x + 3 \)[/tex]
To find the solution, we set these two equations equal to each other because at the intersection, both [tex]\( y \)[/tex] values will be the same.
So,
[tex]\[ 2x - 3 = -x + 3 \][/tex]
Next, let's solve for [tex]\( x \)[/tex]:
1. Combine like terms by adding [tex]\( x \)[/tex] to both sides:
[tex]\[ 2x + x - 3 = 3 \][/tex]
[tex]\[ 3x - 3 = 3 \][/tex]
2. Add 3 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 3x = 6 \][/tex]
3. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 2 \][/tex]
Now that we have [tex]\( x = 2 \)[/tex], we need to find [tex]\( y \)[/tex]. Substitute [tex]\( x \)[/tex] back into one of the original equations. Let's use the first equation:
[tex]\[ y = 2x - 3 \][/tex]
[tex]\[ y = 2(2) - 3 \][/tex]
[tex]\[ y = 4 - 3 \][/tex]
[tex]\[ y = 1 \][/tex]
Therefore, the solution to the system of equations is [tex]\( (2, 1) \)[/tex].
Let's verify this solution by substituting [tex]\( x = 2 \)[/tex] into the second equation:
[tex]\[ y = -x + 3 \][/tex]
[tex]\[ y = -(2) + 3 \][/tex]
[tex]\[ y = -2 + 3 \][/tex]
[tex]\[ y = 1 \][/tex]
This confirms that [tex]\( (2, 1) \)[/tex] is indeed the solution to the system of equations.
Therefore, the correct solution is [tex]\( (2, 1) \)[/tex].
Thus, the answer is:
B. [tex]\( (2, 1) \)[/tex]
