Question

Solve the system of linear equations using the substitution method. 4x+4y=12x=-2y+8

Answer 1

x = -2

y = 5

Explanation:

Solving system of linear equations by substitution method:

4x + 4y = 12

Divide the entire equation by 4,

x + y = 3 -------------(I)

x = -2y + 8 ------------(II)

Substitute x = -2y + 8 in equation (I)

-2y + 8 + y = 3

-2y + y + 8 = 3

Combine like terms,

-y + 8 = 3

Subtract 8 from both sides,

-y = 3 - 8

-y = - 5

Multiply the entire equation by (-1)

`\sf \boxed{\bf y = 5}`

Substitute y= 5 in equation (II),

x = -2*5 + 8

= - 10 + 8

`\sf \boxed{\bf x = -2}`

Answer 2

Hello there. To solve this question, we'll need to isolate a variable, substitute its expression into the other equation and find both values.

4x + 4y = 12

x = -2y + 8

Plug x = -2y + 8 in the first equation. Before doing so, divide both sides of the first equation by a factor of 4

x + y = 3

-2y + 8 + y = 3

Subtract 8 on both sides of the equation and add the values

-2y + y = 3 - 8

-y = -5

Multiply both sides of the equation by a factor of (-1)

y = 5

Plug this value into the expression for x

x = -2 * 5 + 8

Multiply the values

x = -10 + 8

Add the values

x = -2

These are the values we're looking for.

The solution for this system of equation is given by:

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