The system of equations 3x + 2y = 4 and 5x + 4y = 6 has the solutions x = a and y = b. What is the value of 2a + b?

Question

Its a part of my midterm quiz and i really need help please its an online quiz i only have a limited amount of time to answer it.

Answer 1

Sophie,

 

Since it's for a quiz I won't solve it explicitly for you.  But I will walk you through it so you won't be confused by the a & b variables.  You can solve it yourself once the confusion ends.\

 

First, just solve the two equations normally for x & y using either the method of substitution or addition/subtraction. Both x and y solutions will be real numbers since the equations are linear. 

Tip: you will come up with -1 and +2, but I won't tell you which is x and which is y.

 

Second, the x & y solutions, use them to define a & b: a = x and b = y.

 

Finally, using these a & values, compute (2a + b).

Now you're finished. and good luck.

Answer 2

Sophie, this is where you could solve the system by substitution.

 

 3x+2y=4

-3x      -3x

 

2y=4-3x Divide both sides by 2.

 

y=2-3/2*x  Substitute this into the second equation.

 

5x+4(2-3/2x)=6

5x+4*2-4*3/2*x=5x+8-6x=8

-x+8=6

    -8 -8

 

-x=-2 Hence, x=2 This implies a=2. Substitute this into what is y=b.

 

b=2-3/2*2

 

Therefore 2a+b=2*2+2-3/2*2=4+2-3=3

 

Hope this helps.