how do you solve y=2x+3 and y=4x-1?

Answer 1

*Since the y-variables are isolate > set both to equal each other...

2x + 3 = 4x - 1

First: subtract "4x" from both sides...

2x - 4x + 3 = 4x - 4x - 1

- 2x + 3 = - 1

Sec: subtract "3" from both sides...

- 2x + 3 - 3 = - 1 - 3

- 2x = - 4

Third: isolate "x" on one side > divide both terms by "-2"...

-2x/-2 = - 4/-2
x = 2

Fourth: replace "2" with the x-variable in the 1st equation (choose either equation)...

y = 2(2) + 3
y = 4 + 3
y = 7

Solution: (2, 7)

Answer 2

Since y must hold the same value in simultaneous equations and y is set equal to two different expressions involving x, you can set those two expressions equal to each other.
2x + 3 = 4x -1 Subtract 2x from both sides and add 1 to both sides 2x - 2x + 3 + 1 = 4x -2X -1 +1 or simplified 4 = 2x x = 2

Answer 3

If this is a system of two equations:

Get rid of one of the variables by subtracting the equations.

y=4x-1 minus ....
y=2x+3
0 = 2x - 4
4 = 2x
2 = x

Put 2 in for x in either equation.

y = 2*2 + 3
y = 4 + 3
y = 7

Check it by using both values in the other equation.
7 = 4*2 - 1
7 = 8 - 1

OK

Answer 4

y=2x+3
y=4x-1 subtract
0=-2x+4 add 2x to each side
2x=4 divide both sides by 2
x=2
y=2*2+3
y=4+3
y=7

(2, 7)

check

4*2-1=8-1=7=y

Answer 5

enable f ( x ) = y and g ( y ) = x ie g is inverse of f ( 2x + 3 ) y = 4x - a million 2 x y + 3 y = 4 x - a million 2 x ( y - 2 ) = - a million - 3 y x = - ( a million + 3 y ) / ( 2 y - 4 ) g ( y ) = - ( a million + 3 y ) / ( 2 y - 4 ) g ( x ) = - ( a million + 3 x ) / ( 2 x - 4 ) <---------inverse function

Answer 6

set 2x+3 equal to 4x-1 and solve for x...

2x+3 = 4x-1
4 = 2x
x = 2

now plug x = 2 into any equation to get the y-coordinate...

y = 2(2)+3 = 7

final answer...
(2, 7)
or
x=2 and y=7

Answer 7

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

(1)=(2)

2x+3=4x-1
4x-2x=3+1
2x=4
x=2

therefore y=4(2)-1=7

Answer 8

2x+3=4x-1
-2x+3=-1
-2x=-4
x=2

y=2(2)+3
y=4+3
y=7

y=4(2)-1
y=8-1
y=7

The solution set is (2,7)