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)
(6, 2)
To find the solution to the system of equations:
1. Start with the second equation and substitute the value of y into the first equation:
y = -1/2x + 5
2x - (-1/2x + 5) = 10
2x + 1/2x - 5 = 10
Multiplying the entire equation by 2 to eliminate the fraction:
4x + x - 10 = 20
5x - 10 = 20
3. Add 10 to both sides of the equation:
5x = 30
4. Divide both sides of the equation by 5 to solve for x:
x = 6
5. Substitute the value of x back into one of the original equations to solve for y:
y = -1/2(6) + 5
y = -3 + 5
y = 2
Therefore, the solution to the system of equations is (6, 2).
The answer is (6, 2).