Question

What is the solution of the system?
Use the substitution method.
{3x+2y=11
x−2=−4y
a The only solution is (12, −52) .
b The only solution is (4, −12) .
c There is no solution.
d There are an infinite number of solutions.

Answer 1

Answer: (10, -2)

That is, x = 10, y = -2

Step-by-step explanation: Let 3x + 2y = 11 be equation I

Let x -2 = -4y be equation II

We shall use the substitution method like stated above.

From equation II, add 2 to both sides

x = 2 - 4y

Next, substitute for the value of x into equation I

3x + 2y = 11

3(2 - 4y) + 2y = 11

6 - 12y + 2y = 11

6 - 10y = 11

Subtract 6 from both sides of the equation

-10y = 5

Divide both sides of the equation by 5

-2 = y

Next, substitute for the value of y (-2) into equation II

x - 2 = -4(-2)

x - 2 = 8

Add 2 to both sides of the equation

x = 10

Therefore the solution is, (10, -2)