SOLUTION: solve by graphing x-y=2 x+y=6

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Question 34615This question is from textbook
: solve by graphing
x-y=2
x+y=6 This question is from textbook

Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+-1+y+=+2 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F-1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 2/1 = 2.
  • 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 -1/-1 = 1.
  • Equation in slope-intercept form: y=1*x+-2.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-2-8%2C+-2%2B8%2C+1%2Ax%2B-2+%29+

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 1+x+%2B+1+y+=+6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-1%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/1 = 6.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/1 = 6.
  • Slope is -1/1 = -1.
  • Equation in slope-intercept form: y=-1*x+6.
graph%28+500%2C+500%2C+6-8%2C+6%2B8%2C+6-8%2C+6%2B8%2C+-1%2Ax%2B6+%29+

So we can see that the point where the two lines defined by the linear equations in the problem intesect is (4,2)
We can check our answer from the above by:
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+-1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+6+%29%0D%0A++

Any system of equations:


has solution

or



(x=4, y=2}


We again get x=4 and y=2 so we know that our answer is correct.
Hope this helps,
lyra