Question

1. solve each linear system by graphing. write your solution as an ordered pair.

$y = \frac{7}{3}x + 5$
$y = 2x - 4$
$x + 3y = 9$

1. here is the graph for one of the equations in a system of two equations. the solution to the system (4 1) select the equations that could be the other equation in the system.

a. $y = -\frac{1}{4}x + 2$
b. $y = x - 1$
c. $y = -\frac{3}{2}x - 2$
d. $y = \frac{1}{2}x - 1$

Explanation:

Step1: Substitute \( y = 2x - 4 \) into \( x + 3y = 9 \)

We have the second equation \( x + 3y = 9 \). Replace \( y \) with \( 2x - 4 \) from the first equation. So the equation becomes \( x + 3(2x - 4) = 9 \).

Step2: Simplify and solve for \( x \)

First, expand the left - hand side: \( x+6x - 12=9 \). Combine like terms: \( 7x-12 = 9 \). Add 12 to both sides: \( 7x=9 + 12=21 \). Then divide both sides by 7: \( x=\frac{21}{7}=3 \).

Step3: Substitute \( x = 3 \) into \( y = 2x - 4 \) to find \( y \)

Substitute \( x = 3 \) into \( y = 2x-4 \), we get \( y=2\times3 - 4=6 - 4 = 2 \).

Answer:

The solution of the linear system is the ordered pair \((3,2)\)