Question

consider the system of equations.
$3x - 2y = 0$
$x + y = 10$
what is the solution of the system?

a) the solution to the system is $(20, -10)$.

b) the solution to the system is $(3, 7)$.

c) the solution to the system is $(4, 6)$.

d) the solution to the system is $(6, 4)$.

Explanation:

Step1: Solve the system of equations

We have the system:

$$
LATEXBLOCK0
$$

From the second equation \(x + y = 10\), we can express \(y\) as \(y = 10 - x\).

Step2: Substitute \(y = 10 - x\) into the first equation

Substitute \(y = 10 - x\) into \(3x - 2y = 0\):

$$ 3x - 2(10 - x) = 0 $$

Expand the equation:

$$ 3x - 20 + 2x = 0 $$

Combine like terms:

$$ 5x - 20 = 0 $$

Add 20 to both sides:

$$ 5x = 20 $$

Divide both sides by 5:

$$ x = 4 $$

Step3: Find the value of \(y\)

Substitute \(x = 4\) into \(y = 10 - x\):

$$ y = 10 - 4 = 6 $$

So the solution to the system is \((4, 6)\).

Answer:

C) The solution to the system is (4, 6).