SOLUTION: 1. Show and explain the steps to solving the following systems of equations by graphing. For each problem tell the x- and y- intercepts of EACH line and the slope. a. 3x + 2y =

Algebra ->  Graphs -> SOLUTION: 1. Show and explain the steps to solving the following systems of equations by graphing. For each problem tell the x- and y- intercepts of EACH line and the slope. a. 3x + 2y =       Log On


   

Question 34017: 1. Show and explain the steps to solving the following systems of equations by graphing. For each problem tell the x- and y- intercepts of EACH line and the slope.
a. 3x + 2y = 6; 4x - y = 8
b. x + 2y = 4; x - y = 1
c. x - 4y = -4; x + 2y = 8
2. Show and explain the steps to solving the following systems of equations by addition. Show ALL steps involved.
a: 3x - 2y = 23; x + 5y = -15
b. x + 2y = -2; 3x + 2y = -12
c. 3x + 4y = 3; 6x - 2y = 1

Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Next time please only put one problem in each submission.
1. a.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 3+x+%2B+2+y+=+6 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-3%2F2.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/3 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/2 = 3.
  • Slope is -3/2 = -1.5.
  • Equation in slope-intercept form: y=-1.5*x+3.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+3-8%2C+3%2B8%2C+-1.5%2Ax%2B3+%29+
and
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 4+x+%2B+-1+y+=+8 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-4%2F-1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/-1 = -8.
  • Slope is -4/-1 = 4.
  • Equation in slope-intercept form: y=4*x+-8.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+-8-8%2C+-8%2B8%2C+4%2Ax%2B-8+%29+
since in both equations the x intercept is 2, you can plug in 2 for x and solve for y:
3%2A2%2B2y=6
6%2B2y=6
6-6%2B2y=6-6
2y=0
2y%2F2=0%2F2
y=0
You can also check your answer in a variety of ways.
1.b. Do in the same way as above (x=1.33333, y=1.33333)
1.c.Do in the same way as above (x=4, y=2)

2.a
3x+-+2y+=+23
-3(x + 5y = -15)
3x-2y=23
+(-3x-15y=45)
-17y=68
-17y%2F-17=68%2F-17
y=-4
plug in y=-4 in one of the original equations.
x%2B%28-20%29=-15
x-20%2B20=-15%2B20
x=5
We can check by pluging in x and y:
3%285%29-2%28-4%29=23
15%2B8=23
23=23
And in the other equation:
5%2B5%28-4%29=15
5-20=-15
-15=-15
[b]Thus x=5 and y=-4[/b]
2.b. Same process as above (x=-5 and y=1.5)
2.c. Same process as above (x=1%2F3 and y=1%2F2)
Smiles,
lyra