Question

Determine the soultion of the system. show your work.
y=5x- 9
y= 2x+6

Answer 1

solve one for x and substitute that into the second

Answer 2

From equation 1)

\[x = \frac{ y+9 }{ 5 }\]

Answer 3

substituting \(y\) is easy here

Answer 4

so,

\[y = 2*[ \frac{ y+9 }{ 5 } ] + 6\]

Answer 5

Solve for Y, and use that value in either equation to find x.

Answer 6

im lost.. i dont understand any of it

Answer 7

You have 2 equations with 2 unknown variables x and y. You need to find out what values x and y need to be so that both of the equations are true.

Answer 8

So what you can do, as i did above, is solve one equation for x.
Then, as i also did above,
Substitute that x value you solved for into the next equation.

You are left with an equation with one variable. You can solve for that variable.

Answer 9

\[y = 2 * \frac{ y+9 }{ 5 } + 6\]

Answer 10

Multiply everything by 5 to get rid of the fraction.

\[5y = 2(y+9) + 30\]

Answer 11

Distribute the 2 into the parenthesis,

5y = 2y + 18 + 30

Answer 12

separate the variable terms and the number constant terms on separate sides,

5y - 2y = 18 + 30

Answer 13

You are left with,

3y = 48

Answer 14

divide both sides of this by 3
y = 48 / 3

Answer 15

So now you have the value for y

y = 48 / 3
y = 16

Answer 16

Pick any of the first original equations,

y= 5x- 9
y= 2x+6

You already found y = 16
Put y = 16 into either of those equations above to find what the x value is.
For example the first equation.

16 = 5x - 9

x = (16 + 9)/5

Answer 17

another approach
y = y
set them equal and solve for x
substitute this value in either of the original expression for y to get the value
y = 5x -9 and y = 2x + 6
5x -9 = 2x + 6
5x - 2x = 6 + 9
3x = 15
x = 5
y = 5(5) - 9 = 25 - 9 = 16
check in eqn 2
16 = 2(5) + 6 = 16
lhs = rhs
(5, 16)

Answer 18

still lost?