SOLUTION: solve graphically ans algebraically: -2x+3y=6 3x+y=2 <p> write the equation for a solutionline that has points (4,1) and (-2,4) <p> what ordered pair is the y-int

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Question 38010: solve graphically ans algebraically:
-2x+3y=6
3x+y=2


write the equation for a solutionline that has points (4,1) and (-2,4)


what ordered pair is the y-intercept and the x-intercept of the linear equation 2x+3y=6
Answer by lyra(94)   (Show Source): You can put this solution on YOUR website!
Please only put ONE question in each submission!!! I will answer your first question.
By algebra:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 3*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=2. Since , x=0.

Answer: .


By graphing
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/-2 = -3.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/3 = 2.
  • Slope is --2/3 = 0.666666666666667.
  • Equation in slope-intercept form: y=0.666666666666667*x+2.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 2/3 = 0.666666666666667.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 2/1 = 2.
  • Slope is -3/1 = -3.
  • Equation in slope-intercept form: y=-3*x+2.


Hope this helps and feel free to contact me with further questions,
lyra

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