Need answers to math problems( systems of equations)?

Question

3. Solve the following system of equations by graphing.
x - y = 4
2x - 5y = 2

4. Solve the following system of equations by graphing.
y = x
y = 5x


5. Solve the following system of equations by graphing.
y = x + 4
y = 4x + 1

6. Solve the following system of equations by graphing.
3x + 4y = 12
2x + 4y = 8

Example 1:


Solve: y = x + 1 and y = -2x + 4

Solution:
Begin by drawing a couple of tables (one for each equation) and filling them in.


y = x + 1

x y
0 1
2 3
-3 -2



y = -2x + 4

x y
0 4
2 0
-2 8
4 -4



Now, plot those points and draw a line connecting them. Once that has been done, you will see that the lines intersect at (1,2) Therefore, the answer will be the point of intersection (1, 2)

Answer 1

First you need to write all the equations in the form:
y = mx + b

3. y = x - 4 and y = 2/5 x - 2

4. y = x and y = 5x

5. y = x + 4 and y = 4x + 1

6. y = -3/4 x + 3 and y = -1/2 x + 2

From y = mx + b, m represents the slope and b represents the y intercept. Start by drawing the y intercept. Then you can carry on to draw the line either by using the slope, or you can find another point and connect the points. To find another point, let x be some value, say 1, then you can determine the y value by plugging the number in to both the equations. The solution to the system of equations is the intersection between the 2 lines.

Answer 2

I love these!

#3:

multiply the top equation by 2, and then subtract the second equation. So you have:

2x -2y = 8
2x -5y =2
------------
3y = 6
y =2
and then substitute in for y in either equation and solve for x, finding that x = 6

#4:

This is done the same way; you can do it without moving everything to one side, and since you have the same coefficient for y in both equations you don't need to multiply anything:

y = x
y = 5x
--------
0 = -4x

0 = x

and y, therefore, is zero also. Not a very fun answer, but the correct one!

#4 and 5: just graph these lines--convert them to y=mx+b form to make it easier, or pick any two pairs of x,y values for each line that satisfy the equation and connect them with a ruler. The point at which the lines intersect is the answer to the simultaneous system--if they don't intersect (if they are parallel) then the system has no answer; if they are both the same line then there are an infinite number of answers.

Answer 3

Elimination by addition method

x - y = 4- - - - - - -Equation 1
2x - 5t = 2- - - - - Equation 2
- - - - - - - -

Multiply equation 1 by - 2

x - y = 4

- 2(x) - (- 2)(y) = - 2(4)

- 2x - (- 2y) = - 8

- 2x + 2y = - 8

- - - - - - - - - - - -

Elimination of x

- 2x + 2y = - 8
2x - 5y = 2
- - - - - - - - - - - -

- 3y = - 6

- 3y / - 3 = - 6 / - 3

y = - 6 / - 3

y = 2

Insert the y value into equation 1

- - - - - - - - - - - - - -

x - y = 4

x - 2 = 4

x - 2 + 2 = 4 + 2

x = 6

Insert the x value into equation 1

- - - - - - - - - - - - - - - - -

Check for equation 1

x - y = 4

6 - 2 = 4

4 = 4

- - - - - - -

Check for equation 2

2x - 5y = 2

2(6) - 5(2) = 2

12 - 10 = 2

2 = 2

- - - - - - - - -

Both equations balance

The solution set is { 6, 2 }

- - - - - - - - - -s-

Answer 4

i wouldn't be able to graph this here, but i will tell you how you can do it.

#3) take the first equation x-y=4 and graph it. the easiest way is to give 0 once to x and once to y and draw the line.
save way draw 2x-5y = 2. now see where these 2 line cut each other. the x,y of that point is your answer.

good luck

Answer 5

3.
x - y = 4..........(1)
2x - 5y = 2......(2)
Frm (1)
x=4+y
Take y=1,then x=4+1=5
similarly, take y=2,3,4...
Frm (2)
2x=5y+2
=> x=(5y+2)/2
Take y=1,then x=[5(1)+2]/2=(5+2)/2=3.5
similarly, take y=2,3,4...
Plot the points on graph and join then
U w'll get two lines
The point where lines meet w'll b d ans.
the line w'll meet at y=2,x=6


Just solve the equ. similarly for all ques.
BTW ans. will b
4.y=0 x=0
5. y=5 x=1
6. y=0 x=4

Answer 6

%. a variable for Sue's age i.e. s and a variable for Jen's age i.e. j j=s+6 (presently Jen's age is Sue's age + 6) j+4=2(s-5) (In 4 years (j+4), Jen would be 2 cases the age Sue grew to become into 5 years in the past (2(s-5)) Sub in s+6 in for j interior the 2d equation j+4=2(s-5) and resolve for s and you gets Sue's contemporary age Sub Sue's contemporary age back into the equation j=s+6 to get Jen's contemporary age Tack on 4 years to Jen's contemporary age and subtract 5 years fron Sue's contemporary age...you need to be certain that Jen's age in 4 years is two times Sue's age 5 years in the past