Question

What is the solution of the following system using the elimination method? 4x + 3y = 6, 2x + 2y = 5

1) The only solution is (-32, 4)
2) The only solution is (3/2, 4)
3) The only solution is (0, 2)
4) There are an infinite number of solutions
5) There is no solution

Answer 1

To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both of the equations so that the coefficients of one of the variables are the same. In this case, the solution to the system of equations is (x, y) = (-3/2, 4).

Step-by-step explanation:

To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both of the equations so that the coefficients of one of the variables are the same. In this case, we can multiply the second equation by 2 to make the coefficient of y the same as the coefficient of y in the first equation:

4x + 3y = 6

4x + 4y = 10

We can now subtract the second equation from the first equation to eliminate the x variable:

(4x + 3y) - (4x + 4y) = 6 - 10

-y = -4

Simplifying, we have:

y = 4

Substituting y = 4 into one of the original equations, we can solve for x:

2x + 2(4) = 5

2x + 8 = 5

2x = -3

x = -3/2

Therefore, the solution to the system of equations is (x, y) = (-3/2, 4).