Math Problem Statement

Determine if each ordered pair is a solution to the given system. 4 x minus 5 y equals 8 4 x plus 3 y equals 40 a. left parenthesis 7 comma 4 right parenthesis b. left parenthesis negative 3 comma negative 4 right parenthesis Question content area bottom Part 1 a. Is the ordered pair left parenthesis 7 comma 4 right parenthesis a solution to the given​ system? Yes No

Solution

To determine if (7,4)(7, 4) is a solution to the system, we substitute x=7x = 7 and y=4y = 4 into both equations and see if both hold true.

The system is:

  1. 4x5y=84x - 5y = 8
  2. 4x+3y=404x + 3y = 40

Substituting (7,4)(7, 4) into the first equation:

4(7)5(4)=2820=84(7) - 5(4) = 28 - 20 = 8 This is true for the first equation.

Substituting (7,4)(7, 4) into the second equation:

4(7)+3(4)=28+12=404(7) + 3(4) = 28 + 12 = 40 This is also true for the second equation.

Since both equations are satisfied, the ordered pair (7,4)(7, 4) is a solution to the system.

Answer: Yes

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

Substitute the values of x and y into the equations to check if they hold true
Equation 1: 4x - 5y = 8
Equation 2: 4x + 3y = 40

Theorems

Substitution method for verifying solutions of a system of linear equations

Suitable Grade Level

Grades 8-10