Answer:
(4, 6)
Step-by-step explanation:
<u>Substitution</u>
Using the second equation, we can substitute for y in the first equation.
4x -(2x-2) = 10
2x +2 = 10 . . . . simplify
x +1 = 5 . . . . . . .divide by 2
x = 4 . . . . . . . . . subtract 1
y = 2(4) -2) = 6 . . . . substitute for x in the equation for y
The solution is (x, y) = (4, 6).
__
<u>Elimination</u>
Often, we like to start with both equations in standard form when we solve by elimination. That is nice, but not completely necessary.
We can eliminate the y-variable by simply adding the two given equations.
(4x -y) +(y) = (10) +(2x -2)
4x = 8 + 2x . . . . . collect terms. The y-variable has been eliminated.
2x = 8 . . . . . . . . . subtract 2x
x = 4 . . . . . . . . . . divide by 2
Y can be found using the second equation.
(x, y) = (4, 6)
__
We could have eliminated the x-variable by multiplying the second equation by 2, then adding the two equations.
(4x -y) +2(y) = (10) +2(2x -2)
y = 6 . . . . . . . . . subtract 4x from both sides. The x-variable has been eliminated.
Now, x can be found using either equation.
6 = 2x -2 . . . substitute for y in the second equation
3 = x - 1 . . . divide by 2
x = 4 . . . . . add 1
(x, y) = (4, 6)
is acute, then slope is positive;