Let's solve this system of equations step by step, just like we would in class!

We have two equations:

1. ( y = 2x - 1 )
2. ( y = -x + 5 )

Step 1: Use substitution (since both equal ( y ))

Since both expressions on the right side equal ( y ), they must equal each other. This is the substitution method!
Set them equal:
( 2x - 1 = -x + 5 )

Step 2: Solve for ( x )

Let’s get all ( x ) terms on one side and constants on the other:

• Add ( x ) to both sides: ( 2x + x - 1 = -x + x + 5 ) → ( 3x - 1 = 5 )
• Add 1 to both sides: ( 3x -1 +1 =5 +1 ) → ( 3x =6 )
• Divide both sides by 3: ( x = 2 )

Step 3: Find ( y )

Now plug ( x=2 ) into either original equation (let’s pick the first one):
( y = 2(2) -1 = 4 -1 =3 )

Check with the second equation to be sure: ( y = -2 +5 =3 ) → same result!

Final Answer

The solution is the point where the two lines cross: ( (2, 3) ).

Great job following along—you’ve got this!

作者声明:本文包含人工智能生成内容。