Solve the system by substitution?

Question

Given f(x) = –5x – 1, find f(a – 4).
A) –5a + 19
B) –5a – 5
C) a – 10
D) a + 19

Solve the system by graphing.
x – y = 5
x + y = 3

Solve the system by addition.
x + y = 4
x – y = 6

Solve the system by addition.
–2x – 3y = –17
x + 4y = 16

Solve the system by substitution.
x + y = 12
y = 2x

Solve the system by substitution.
x – 4y = –19
–4x – 5y = 13

Answer 1

Hi,

Given f(x) = –5x – 1, find f(a – 4).
f(a - 4) = -5(a - 4) - 1 = -5a + 20 - 1 = -5a + 19

A)–5a + 19 <== answer
B)–5a – 5
C)a – 10
D)a + 19

Solve the system by graphing.
x – y = 5
x + y = 3

Solve each equation for y to get the equations in the form y = mx + b, where m is the slope and b is the y intercept.


x - y = 5 becomes y = x - 5. The slope is 1 and the y intercept is -5. This starts on the y axis at -5 and goes up one square and one to the right, over and over.

x + y = 3 becomes y = -x + 3. The slope is -1 and the y intercept is 3. This starts on the y axis at 3 and goes down one square and one to the right, over and over.

The point where the 2 lines cross is the solution. It is at (4,-1).


Solve the system by addition.
x + y = 4
x – y = 6 Add these.
------------
2x = 10
x = 5

Putting 5 in for x, solve for y in either equation.
x + y = 4
5 + y = 4
y = -1
So the answer is (5,-1).


Solve the system by addition.
–2x – 3y = –17
x + 4y = 16 Multiply this equation by 2. then add equations.

–2x – 3y = –17
2(x + 4y = 16)

–2x – 3y = –17
2x + 8y = 32
---------------------
5y = 15
y = 3

Putting 5 in for y, solve for x in either equation.
x + 4y = 16
x + 4(5) = 16
x + 20 = 16
x = -4
So the answer is (-4,3).



Solve the system by substitution.
x + y = 12
y = 2x

x + 2x = 12
3x = 12
x = 4
Putting 4 in for x, solve for y in either equation.
y = 2(4)
y = 8
So the answer is (4,8).


Solve the system by substitution.
x – 4y = –19
–4x – 5y = 13

Solve 1st equation for x: x = 4y - 19
Now substitute this into 2nd equation.
-4(4y - 19) - 5y = 13
-16y + 76 - 5y = 13
-21y + 76 = 13
-21y = -63
y = 3
Putting 3 in for y, solve for x in either equation.
x – 4y = –19
x - 4(3) = -19
x - 12 = -19
x = -7
So the answer is (-7,3).


I hope that helps!! :-)

Answer 2

I guess you're asking us to solve all of these for you, but that's a lot. Here are some examples and things you need to know in order to do these problems:
1. If f(x)=2x+1, then f(a)=2a+1, so you substitute whatever is in the parentheses where the x is, also f(a+1)=2(a+1)+1=2a+2+1=2a+3, so out comes a new expression.
2. If x + 2y = 5 then 2x + 4y = 10 and -3x - 6y = -15 are all the EXACT SAME THING. So, when doing the "addition" method in the 4th problem you listed, you'll have to multiply one equation (or both) by some number so that when you add the equations together, either all the x's or all the y's will go away:
example:
solve x + 2y = 4
-3x + 3y = 2
to eliminate the x's, since there are -3 of them in the bottom equation, you would need 3 of them in the top equation so that when you add the equations together, you get 0 x's: multiplying everything in the top equation by 3 gives
3x + 6y = 12 <---- new 1st equation
-3x+3y = 2 <-----same 2nd equation
------------------------
9y = 14 <----------now you can solve for y

3. to graph, you can either use Intercepts or change both of the equations to the Slope-Intercept Form, y=mx+b so you can graph them. You should NOT plot points. Make sure to practice doing these without plotting points.
remember that y=mx+b, m=slope = y/x, and b is the y-intercept, where the graph hits the y-axis
example: -2x+y=4
A) Intercepts: If x=0, y=4 (this gives one point). If y=0, then x=-2 (this gives another point) Graph those two points and draw a line between them.
B) Change to y=2x+4. Start at y=4 on the y=axis. the slope of 2 is the same as 2/1 meaning you go up 2 and to the right 1 to get to the next point. once you have those two points, connect them to get your graph.
4. Substitution is solving for one letter in one equation and plugging what you get into the OTHER equation.
example:
solve 2x+y=4 and 3x -2y=8
use the first equation and solve for y, giving you y=4-2x
now, put 4-2x in where the y is in the second equation:
3x-2(4-2x)=8. now that you only have one letter there, x, you can solve for x. don't forget to distribute the -2!!!
Hope this helps! Let me know if you have any other questions.

Answer 3

I have enough time to do all of these, so here we go:

1. f(x)=-5x-1, you are looking for f(a-4)

Substitute x with a-4 to get:

-5(a-4)-1

Now distribute and simplify:


-5a+20-1

The answer is -5a+19 (A)

2. I can't graph this system for you, because there is no way how to do it here.Just graph the two lines and you will see they intersect at (4,-1)

3. To solve by addition, or simply by elimination, eliminate the y's and add the x and 6+4

You will have 2x=10, x=5

Now find y: 5+y=4

y=-1, so the answer is (5,-1), put the answer in the second equation to check your answer.

4. This one can be tough here, but no problem. Here you have to figure what variable you want to eliminate. Since x is opposite of each other, we'll eliminate x. But we have to get the coefficients the same. On the second equation, multiply the entire equation by 2 to get:

-2x-3y=-17
2x+8y=32

Eliminate the x to get: 5y=15
Solve for y: y=3

Now substitute y in the first equation with 3 and solve for x:

-2x-3(3)=-17

-2x-9=-17

-2x=-8

x=4

Your answer is (4,3)

Substitute you x and y values in the second equation to check your answer.

5. This one is easy: Substitute y with 2x in the first equation:

You get: x+2x=12

Now solve for x: 3x=12

x=4

Now substitute x with 4 and solve for y: 4+y=12

y=8

The answer is (4,8). Be sure to check your answer.

6. Find a variable that you want to substitute. Since no variable is left alone, we must make one alone. since x does not have a coefficient in the first equation, we'll solve the equation for x and substitute x, like so:

x=4y-19
-4x-5y=13

Now substitute x into the second equation and solve for y:

-4(4y-19)-5y=13

-16y+76-5y=13

-21y+76=13

-21y=-63

y=3

Now substitute y with 3 in the first equation and solve for x:

x-4(3)=-19

x-12=-19

x=-7

You answer is (-7,3). Check you answer.

Whew! We're done.

Answer 4

no longer complicated: 3x + 4y = -sixteen, 3x + 11 = y... or; 3x - y = -11 Subtract out the 2d equation from the 1st. 5y = -5 y = -a million And now resolve for x: 3x + 4y = -sixteen, 3x + 11 = y 3x + (-4) = -sixteen, 3x + 11 = (-a million) 3x = -12, 3x = -12 x = -4, x = -4 y = -a million and x = -4 No mistaking it from the above. that's an ironclad information!

Answer 5

The first is A. The rest can't really be shown, but the answers are all pretty easy if you get some help.

Answer 6

f(x)=-5x-1
f(a-4)=-5(a-4)-1
=-5a+20-1
f(a-4) =-5a +19 -----i.e.,(A)

x-y=6-----------(1)
x+y=4----------(2)
Adding(1) & (2) ,we have
2x=10
or x=5
Mutiplying (1)by -1 ,we have
-x+y=-6---------(3)
Adding(2) &(3),we have,
2y=-2 or y=-1
so x=5 &y=-1 ans

Answer 7

f(a-4)=-5(a-4)-1,
...=-5a+19 (A)