equations and such HELP?

Question

state answer as an ordered pair (x,y)

1. x+y=1
y=(2/3)x-4

2. Is this ordered pair (5.3, 1.2) a solution to the system?
x+2y=1
x-3y>=0
yes or no?

3. Fill in the blank with correct word
In systems of equations, solving one equation for a variable and plugging that expression into another equation is known as the what method?

4. Solve the following system of equations. WHat is the value of a?
3a-5b=10
a+7b=12
a)a=5
b)a=79/13
c)a=1
d) none of these

5.) Solve the following systems of equations. Describe the graph without graphing.
3x-2y=24
6x-4y=-6
a)two intersecting lines-solution in quadrant 1
b)two intersecting lines-solution in quadrant 3
c)two parallel lines-no solution
d)coincidental lines-many solutions

6. Describe the graph without graphing.
a+b=10
3a+2b=40
a)two intersecting lines-solution in quadrant 2
b)two intersecting lines-solution in quadrant 4
c)two parallel lines-no solution
d)coincidental lines-many solutions

Answer 1

I'll solve 1 and 4 and just give the answer to the others.

Answer 1:

x + y = 1 ..... (1)
y = (2x/3) - 4 ..... (2)

From (1),
y = 1 - x ..... (3)

Substitute (3) in (2),

1 - x = (2x/3) - 4
1 - x = (2x - 12)/3
3 - 3x = 2x - 12
5x = 15
x = 3

Put x = 3 in (3),

y = 1 - 3
y = -2.

x = 3, y = -2

Ordered pair ---> (3, -2)



Answer 2:
No (You can find out by substituting the values into the equations. The ordered pair satisfies only the second equation/inequality)

Answer 3:
Substitution method


Answer 4:
3a - 5b = 10 ..... (1)
a + 7b = 12 ..... (2)

From (1),
3a = 5b + 10
a = (5b + 10)/3 ..... (3)

Put (3) in (2),
[(5b + 10)/3] + 7b = 12
(26b + 10)/3 = 12
26b + 10 = 36
26b = 26
b = 1

Put b = 1 in (3),

a = (5 + 10)/3
a = 15/3
a = 5

c) a = 5 is the answer



Answer 5:
Two parallel lines

Answer 6:
a = 20, b = -10

If a is represented by x - axis, Option b is correct
If a is represented by y-axis, Option A is correct.




Feel free to send me a note if you have any doubts regarding this topic.

Answer 2

you are able to the two use a table of values and basically plug in values and then graph hence, which includes... plug in -2, -a million, 0, a million, 2 for x, and sparkling up for y. then graph. or verify its in slope intercept form... y=mx+b..which that's.. and graph from there. to do this, you employ b through fact the y intercept. hence we've y=3x+0. so b=0. so as which potential we initiate up the place the y intercept is 0. which it the beginning place. (0,0) then next is the slope. m=slope, on your equation m=3. so the slope is 3/a million, which potential from the beginning place you will flow up 3 areas and over to the incredible a million area. then repeat to get the graph of your equation. ought to be a straight away line.

Answer 3

1. (3, -2)
2. no
3. substitution
4. a) a=5
5. c)
6. d)