Final answer:
The intersection of the two equations x+5y=8 and -x+2y=-1 is x = 3 and y = 1.
Step-by-step explanation:
To find the intersection of the two equations, we can solve the system of equations using either substitution or elimination method. Let's use the elimination method.
Multiply the second equation by 2: -2x + 4y = -2.
Add the two equations together: (x + 5y) + (-2x + 4y) = 8 + (-2).
Simplify: -x + 9y = 6.
Next, multiply the first equation by -1: -x - 5y = -8.
Add the new equation to the previous one: (-x + 9y) + (-x - 5y) = 6 + (-8).
Simplify: -2x + 4y = -2.
Now we have a new system of equations: -x + 9y = 6 and -2x + 4y = -2.
To solve this system, we can multiply the first equation by 2 and subtract it from the second equation: (-2x + 4y) - (2(-x + 9y)) = -2 - 2(6).
Simplify: -2x + 4y + 2x - 18y = -2 - 12.
Combine like terms: -14y = -14.
Divide both sides by -14: y = 1.
Substitute the value of y back into one of the original equations to solve for x: x + 5(1) = 8.
Simplify: x + 5 = 8.
Subtract 5 from both sides: x = 3.
So, the intersection of the two equations is x = 3 and y = 1.