4x + y = 7 2x + 5y = -1 This question is about solving linear systems algebraically
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4x + y = 7
2x + 5y = -1
To solve this system algebraically, use substitution.
Solve the first equation for y.
4x + y = 7
y = 7 - 4x
Substitute this expression in for y in the second equation and solve for x.
2x + 5y = -1
2x + 5(7 - 4x) = -1
2x + 35 - 20x = -1
-18x + 35 = -1
-18x = -36
x = 2
Now substitute 2 in for x in the first equation and solve for y.
4x + y = 7
4 * 2 + y = 7
8 + y = 7
y = -1
The solution to this system is {x = 2, y = -1}. Substitute these values into the second equation to check for accuracy.
2x + 5y = -1
2 * 2 + 5 * -1 = -1
4 + -5 = -1
-1 = -1
The solution {x = 2, y = -1} is correct.
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