SOLUTION: You guys have been so great and a life saver to one who is "math illiterate" like me. Do you know the answer to the question (5, 1) is a solution to 2x - 3y = 7. The answer must

Algebra ->  Coordinate-system -> SOLUTION: You guys have been so great and a life saver to one who is "math illiterate" like me. Do you know the answer to the question (5, 1) is a solution to 2x - 3y = 7. The answer must      Log On


   

Question 368863: You guys have been so great and a life saver to one who is "math illiterate" like me.
Do you know the answer to the question (5, 1) is a solution to 2x - 3y = 7. The answer must be explained in verbal terms, although plotting it first on a graph would be helpful.
Again, thanks a million.
Monica
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!
The point (5,1) is a solution to the equation 2x-3y=7 if and only if when replacing the variables x and y with 5 and 1 respectively, you end up with a true statement.

So, we will use 2x-3y=7 and replace the x's with 5 and the y's with 1:

2x-3y=7

2*(5)-3*(1)=7

10-3=7

7=7 this is a TRUE statement!

Therefore, we are assured that the point (5,1) IS indeed a solution to the equation 2x-3y=7

Also, see the graph and more details below, I hope this helps!

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 2+x+%2B+-3+y+=+7 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-2%2F-3.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 7/2 = 3.5.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 7/-3 = -2.33333333333333.
  • Slope is -2/-3 = 0.666666666666667.
  • Equation in slope-intercept form: y=0.666666666666667*x+-2.33333333333333.