Questions: Solve the given system by the substitution method. 2x + y = 11 7x - 3y = 19

Solve the given system by the substitution method. 2x + y = 11 7x - 3y = 19
Transcript text: Solve the given system by the substitution method. \[ \left\{\begin{array}{l} 2 x+y=11 \\ 7 x-3 y=19 \end{array}\right. \]
failed

Solution

failed
failed

Solution Steps

To solve the given system of equations using the substitution method, follow these steps:

  1. Solve one of the equations for one variable in terms of the other variable.
  2. Substitute this expression into the other equation to solve for the second variable.
  3. Substitute the value of the second variable back into the first equation to find the value of the first variable.
Step 1: Solve the first equation for \( y \)

Given the system of equations: \[ \left\{\begin{array}{l} 2x + y = 11 \\ 7x - 3y = 19 \end{array}\right. \]

First, solve the equation \( 2x + y = 11 \) for \( y \): \[ y = 11 - 2x \]

Step 2: Substitute \( y \) into the second equation

Substitute \( y = 11 - 2x \) into the second equation \( 7x - 3y = 19 \): \[ 7x - 3(11 - 2x) = 19 \]

Step 3: Simplify and solve for \( x \)

Simplify the equation: \[ 7x - 33 + 6x = 19 \] Combine like terms: \[ 13x - 33 = 19 \] Add 33 to both sides: \[ 13x = 52 \] Divide by 13: \[ x = 4 \]

Step 4: Substitute \( x \) back into the expression for \( y \)

Substitute \( x = 4 \) back into \( y = 11 - 2x \): \[ y = 11 - 2(4) = 11 - 8 = 3 \]

Final Answer

\(\boxed{(x, y) = (4, 3)}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Determine whether the following equation defines y as a function of x x^2 + y^2 = 144 Does the equation x^2 + y^2 = 144 define y as a function of x?
failedAnswered
A ball is launched vertically upward with a velocity of 256 ft / s, so its position function can be modeled as s(t)=-16 t^2+256 t. What is the velocity of the ball when it first reaches a vertical height of 880 ft?
failedAnswered
Module 2 Homework Begin Date: 8/26/2024 12:01:00 AM Due Date: 9/9/2024 11:59:00 PM End Date: 9/10/2024 11:59:00 PM Problem 6: (13% of Assignment Value) Three capacitors and a battery are connected as shown. The capacitance values are C1=9.6 μF, C2=5.2 μF, and C3=7.8 μF. The battery voltage is V0=12 V. Part (a) Enter an expression for the equivalent capacitance, C12, of the two capacitors C1 and C2 in terms of the variables given in the problem statement. C12=
failedAnswered
When solving systems of equations, you can check your answer by: Substituting the values of the variables into the first equation and then simplifying to make sure that you get a true statement. Substituting the values of the variables into the second equation and then simplifying to make sure you get a true statement. Substituting the values of the variables into both equations and then simplifying to make sure that you get two true statements.
failedAnswered
La masa molar del permanganato de potasio (KMnO4) es 158 g / mol. ¿Cuál será la concentración molar de una solución acuosa que contiene 79 g de permanganato de potasio en 100 mL? A) 0.5 mol / L B) 5,0 mol / L C) 7,0 mol / L D) 10,0 mol / L