SOLUTION: Write a system of linear equations that has (-1,4) as its only solution. Verify that (-1,4) is a solution using either the substitution method or the elimination method.

Question 849480: Write a system of linear equations that has (-1,4) as its only solution. Verify that (-1,4) is a solution using either the substitution method or the elimination method.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write a system of linear equations that has (-1,4) as its only solution.
Verify that (-1,4) is a solution using either the substitution method or the elimination method.
:
Select -3 as the slope, then write an equation using the coordinates -1,4
y = 3x + b
replace x and y, find b
4 = -3(-1)+b
4 = 3 + b
4 - 3 = b
b = 1
y = -3x + 1
in standard form
3x + y = 1
:
Select another slope 2, find another equation with the same coordinates
y = 2x + b
4 = 2(-1) + b
4 = -2 + b
4 + 2 = b
b = 6
y = 2x + 6
in standard form
-2x + y = 6
:
solve using eliminaion
-2x + y = 6
3c + y = 1
-------------Subtraction eliminates y, find x
-5x + 0 = 5
x = 5 /-5
x = -1
find y
-2(-1) + y = 6
2 + y = 6
y = 6 - 2
y = 4
:
The only solution for 3x + y = 1 and -2x + y = 6, is -1,4
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