Question

Solve the system of equations.3x+y=2 7x−4y=30 (1 point)Responses(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 substitution or elimination. Let's solve for \( y \) in Equation 1:

From Equation 1: \[ y = 2 - 3x \]

Now we can substitute this expression for \( y \) into Equation 2:

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

Simplify: \[ 7x - 8 + 12x = 30 \] \[ 19x - 8 = 30 \] Add \( 8 \) to both sides: \[ 19x = 38 \] Now divide by \( 19 \): \[ x = 2 \]

Now substitute \( x = 2 \) back into the expression 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).