Question

Y=x+12
4x+2y=27
Solve each system of equation algebraically

Answer 1

To solve the system of equations algebraically, we use the method of substitution. The value of x is 1/2 and the value of y is 25/2.

Step-by-step explanation:

To solve the system of equations algebraically, we can use the method of substitution. First, we can solve the first equation for y in terms of x: y = x + 12. Then, we substitute this expression for y in the second equation: 4x + 2(x + 12) = 27. Simplifying, we get 6x + 24 = 27. Subtracting 24 from both sides, we have 6x = 3. Finally, dividing both sides by 6, we find x = 1/2. Plugging this value back into the first equation, we can solve for y: y = 1/2 + 12, which gives us y = 25/2.

Answer 2

Solve by Substitution :

// Solve equation [1] for the variable y

[1] y = x + 12

// Plug this in for variable y in equation [2]

[2] 2•(x +12) + 4x = 27 [2] 6x = 3

// Solve equation [2] for the variable x

[2] 6x = 3 [2] x = 1/2

// By now we know this much :

y = x+12 x = 1/2

// Use the x value to solve for y

y = (1/2)+12 = 25/2 Solution : {y,x} = {25/2,1/2} y=x+12;4x+2y=27 Solution : {y,x} = {25/2,1/2} System of Linear Equations entered : [1] y=x+12 [2] 4x+2y=27 Equations Simplified or Rearranged : [1] y - x = 12 [2] 2y + 4x = 27