Consider the system of equations.
y = -2x + 1
y = 3x – 4
Determine the correct graph of the system. Then, determine the correct solution.
(-1,1)
(1,-1)
(-1,-1)
(1,1)
Consider the system of equations.
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To find the solution of the system of equations, we can set the two equations equal to each other:
1. From the first equation: ( y = -2x + 1 )
2. From the second equation: ( y = 3x – 4 )
Setting them equal to each other:
[
-2x + 1 = 3x – 4
]
Now, let’s solve for ( x ):
1. Add ( 2x ) to both sides:
[
1 = 5x – 4
]
2. Add ( 4 ) to both sides:
[
5 = 5x
]
3. Divide both sides by ( 5 ):
[
x = 1
]
Now substitute ( x = 1 ) back into one of the original equations to find ( y ). I’ll use the first equation:
[
y = -2(1) + 1 = -2 + 1 = -1
]
So, the solution to the system of equations is ( (1, -1) ).
In conclusion, the correct solution is ( (1, -1) ).