Question

topic 4 lesson 2 - solving systems by subst
1.
$y = -2$
$5x - 3y = 16$

Explanation:

Step1: Identify given equations

The system is:
$y = x - 2$
$2x + 3y = 16$

Step2: Substitute $y$ into second equation

Replace $y$ with $x-2$ in $2x + 3y = 16$:
$2x + 3(x - 2) = 16$

Step3: Simplify and solve for $x$

Expand and combine like terms:
$2x + 3x - 6 = 16$
$5x - 6 = 16$
$5x = 22$
$x = \frac{22}{5} = 4.4$

Step4: Solve for $y$ using $y=x-2$

Substitute $x=\frac{22}{5}$:
$y = \frac{22}{5} - 2 = \frac{22}{5} - \frac{10}{5} = \frac{12}{5} = 2.4$

Answer:

$x=\frac{22}{5}, y=\frac{12}{5}$ or $x=4.4, y=2.4$