5x+2y=7. 4x+y=8 systems of equations substitution method

x=3 and y=−4

Step-by-step explanation:

Solve4x+y=8for y:

4x+y=8

4x+y+−4x=8+−4x(Add -4x to both sides)

y=−4x+8

Step: Substitute−4x+8 for y in 5x+2y=7:

5x+2y=7

5x+2(−4x+8)=7

−3x+16=7(Simplify both sides of the equation)

−3x+16+−16=7+−16(Add -16 to both sides)

−3x=−9

-3x/-3=-9/-3

(Divide both sides by -3)

Step 2: Substitute 3 for x in y=−4x+8:

y=−4x+8

y=(−4)(3)+8

y=−4(Simplify both sides of the equation)

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2