Question

Pleaseeeee helppppp

What is the solution to the system of equations below?
2 x minus y = 10 and y = negative one-half x + 5
(6, 2)
(6, –2)
(–6, –22)
(–6, 8)

Answer 1

(a) (6, 2)

Explanation:

The system of equations has one of them in y= form, so it lends itself to solution by substitution.

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Using the equation for y to substitute into the first equation, we have ...

2x -y = 10

2x -(-1/2x +5) = 10 . . . . . substitute for y

2x +1/2x -5 = 10 . . . . . eliminate parentheses

5/2x = 15 . . . . . . . . . add 5, collect terms

x = 6 . . . . . . . . . . . multiply by 2/5

Using the equation for y, we have ...

y = -1/2(6) +5 = -3 +5

y = 2

The solution is (x, y) = (6, 2).