Question

Solve.

{4x+y=53
{x+y=3

Use the linear combination method.




(−3, 7)


(2, −3)


(0, 5)


(0, −3)

Answer 1

To solve the system of equations using the linear combination method, multiply one equation to make the coefficients of one variable equal, then subtract the equations to eliminate that variable. Finally solve for the remaining variable to find the solution.

Step-by-step explanation:

To solve the system of equations using the linear combination method, we need to eliminate one variable by multiplying the equations by appropriate constants and then adding or subtracting them. Let's start with the given equations:

Equation 1: 4x + y = 53

Equation 2: x + y = 3

Multiply Equation 2 by 4 to make the coefficients of y equal:

4(x + y) = 4(3)

4x + 4y = 12

Now, subtract Equation 1 from the modified Equation 2:

(4x + 4y) - (4x + y) = 12 - 53

3y = -41

Divide both sides of the equation by 3 to solve for y:

y = -41/3

Substitute the value of y into Equation 2 to find x:

x + (-41/3) = 3

Simplify the equation:

x = 22/3

Therefore, the solution to the system of equations is (x, y) = (22/3, -41/3).

Answer 2

(2, -3)

Step-by-step explanation:

Apparently, the equations are supposed to be ...

• 4x +y = 5
• 3x +y = 3

The solution for x can be found by subtracting the second equation from the first:

(4x +y) -(3x +y) = (5) -(3)

x = 2 . . . . . . . matches the second answer choice

Y can be found from either equation:

y = 5 - 4x . . . . . subtract 4x from the first equation

y = 5 -4(2) = -3

The solution is (x, y) = (2, -3).