Solve the system of equations. 3x+y=2 7x−4y=30 (1 point)

Question

(12, 12) left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

(2, −4) left parenthesis 2 comma negative 4 right parenthesis

(−2, 8) left parenthesis negative 2 comma 8 right parenthesis

(2, −2)

Answer 1

To solve the system of equations:

1. \( 3x + y = 2 \) (Equation 1)
2. \( 7x - 4y = 30 \) (Equation 2)

We can use the substitution or elimination method. Let's use substitution.

From Equation 1, we can express \( y \) in terms of \( x \):

\[ y = 2 - 3x \]

Now, substitute \( y \) into Equation 2:

\[ 7x - 4(2 - 3x) = 30 \]

Distributing the \(-4\):

\[ 7x - 8 + 12x = 30 \]

Combining like terms:

\[ 19x - 8 = 30 \]

Adding 8 to both sides:

\[ 19x = 38 \]

Dividing by 19:

\[ x = 2 \]

Now, substitute \( x = 2 \) back into the equation for \( y \):

\[ y = 2 - 3(2) = 2 - 6 = -4 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (2, -4) \]

So the answer is:

(2, -4)