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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