Question

Use substitution to solve the system.5x-4y = -30–2x+y = 9 x= y=

Answer 1

Step-by-step explanation:

Consider the following system of linear equations:

Equation 1:

`5x-4y=-30`

Equation 2:

`-2x+y=9`

From equation 2, we can solve for y and obtain the following equation:

Equation 3:

`y=9+2x`

Now, replacing this in equation 1, we get:

`5x-4(9+2x)=-30`

applying the distributive property, we get:

`5x\text{ - 36 - 8x = -30}`

putting like terms together, we obtain:

`5x\text{ - 8x = -30 + 36}`

this is equivalent to:

`\text{ - 3x = 6}`

solving for x, we get:

`x=\text{ -}(6)/(3)=\text{ - 2}`

Now, replacing this value in equation 3, we get:

`y=9+2x=\text{ 9 + 2\lparen-2\rparen= 9 - 4 = 5}`

we can conclude that the correct answer is:

Answer:

The solution of the given system of linear equations is:

( x , y ) = ( - 2, 5 )

then

x= - 2

and

y = 5