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 =
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
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. 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.
since in both equations the x intercept is 2, you can plug in 2 for x and solve for y:
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
-3(x + 5y = -15)
3x-2y=23
+(-3x-15y=45)
plug in y=-4 in one of the original equations.
We can check by pluging in x and y:
And in the other equation:
[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 ( and )
Smiles,
lyra