Systems of Linear Equations Online Practice

Question

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7 of 137 of 13 Items

Question
Solve the system of equations.
x−3y=18

7x−5y=46
(1 point)
Responses

(105, 5)
left parenthesis 105 comma 5 right parenthesis

(33, 5)
left parenthesis 33 comma 5 right parenthesis

(3, −5)
left parenthesis 3 comma negative 5 right parenthesis

(−3, −5)
left parenthesis negative 3 comma negative 5 right parenthesis

Answer 1

To solve the given system of equations:

1. \( x - 3y = 18 \) (Equation 1)
2. \( 7x - 5y = 46 \) (Equation 2)

Let's solve these equations step by step.

Step 1: Solve for \( x \) in terms of \( y \) using Equation 1.

From Equation 1: \[ x = 3y + 18 \]

Step 2: Substitute \( x \) into Equation 2.

Substituting \( x \) in Equation 2 gives: \[ 7(3y + 18) - 5y = 46 \]

Step 3: Expand and simplify.

\[ 21y + 126 - 5y = 46 \] Combine like terms: \[ 16y + 126 = 46 \]

Step 4: Solve for \( y \).

Subtract 126 from both sides: \[ 16y = 46 - 126 \] \[ 16y = -80 \] \[ y = -5 \]

Step 5: Substitute \( y \) back into Equation 1 to find \( x \).

Now substitute \( y = -5 \) back into the equation for \( x \): \[ x = 3(-5) + 18 \] \[ x = -15 + 18 \] \[ x = 3 \]

Final Solution

So, the solution of the system of equations is: \[ (x, y) = (3, -5) \]

Answer

The correct response is: (3, -5)