Use the substitution method to solve the following system of equations:
1. [tex]y = 2x - 5[/tex]
2. [tex]4x - y = 7[/tex]
Attempted solution:
Substitute [tex]y[/tex] from equation 1 into equation 2:
[tex]4x - (2x - 5) = 7[/tex]
Simplify the equation:
[tex]2x + 5 = 7[/tex]
[tex]2x = 2[/tex]
[tex]x = 1[/tex]
What was the mistake in the initial attempt?
Answer (2)
It should be 4x-(2x-5)=7.
4 x − ( 2 x − 5 ) = 7 4 x − 2 x + 5 = 7 2 x = 2 x = 1
The mistake in the initial attempt was in not correctly isolating the variable after combining terms. The correct solution shows that x = 1 and substituting this back gives y = − 3 . Careful attention to arithmetic steps is essential in solving equations.
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