Answer the questions and complete the steps to solve the system of equations below.

Question

3x + 2y = 16
y=x+3
a) Which variable should you substitute for in the equation 3x + 2y = 16?
choose your answer...
b) What value can be substituted for that variable? choose your answer...
c) Rewrite the equation with the substitution. choose your answer...
choose your answer...
3(x+3) + 2y =16
• x into the equation and solve for y.
3x + 2(x+3) = 16

Answer 1

To solve the system of equations, let's go through the steps one by one.

1. Identify which variable to substitute:

   The second equation is $y=x+3$. It is convenient to substitute for $y$ in the first equation because it directly gives $y$ in terms of $x$.

   a) Which variable should you substitute for in the equation $3x+2y=16$?
   Answer: $y$

2. What value can be substituted for that variable?

   From the second equation, we have $y=x+3$.

   b) What value can be substituted for that variable?
   Answer: $x+3$

3. Rewrite the equation with the substitution:

   Replace $y$ in the first equation with $x+3$.

   c) Rewrite the equation with the substitution.

   Start with the original equation: $$3x+2y=16$$ Substitute $y$ with $x+3$: $$3x+2(x+3)=16$$

4. Now, simplify and solve for $x$:

   $$3x+2(x+3)=16$$ Expanding this: $$3x+2x+6=16$$ Combine like terms: $$5x+6=16$$

   Next, isolate $x$ by subtracting 6 from both sides: $$5x=10$$

   Finally, divide by 5: $$x=2$$

5. Substitute $x=2$ back into the $y$ equation to find $y$:

   $$y=x+3=2+3=5$$

Thus, the solution to the system of equations is: $$(x,y)=(2,5)$$

Answer 2

Answer the questions and complete the steps to solve the system of equations below.
3x + 2y = 16
y =x+3
a) Which variable should you substitute for in the equation 3x + 2y = 16?
choose your answer...
b) What value can be substituted for that variable? choose your answer... V
c) Rewrite the equation with the substitution. choose your answer...
d) Solve the equation for x.
e) Substitute that value for x into the equation and solve for y.
f) Use substitution to check your solution for the system.

Answer 3

Let’s go through the process step-by-step based on the given system of equations:

• Equation 1: $3x+2y=16$
• Equation 2: $y=x+3$

a) Which variable should you substitute for in the equation $3x+2y=16$?

Since Equation 2 expresses $y$ in terms of $x$, it is most convenient to substitute for $y$ in Equation 1.

Answer: $y$

b) What value can be substituted for that variable?

From Equation 2, $y$ can be replaced with $x+3$.

Answer: $x+3$

c) Rewrite the equation with the substitution.

Now, substitute $y$ in Equation 1 with $x+3$:

Starting with: $$3x+2y=16$$ Substituting $y$: $$3x+2(x+3)=16$$

d) Solve the equation for $x$.

Now, we will simplify and solve for $x$: $$3x+2(x+3)=16$$ Expanding this: $$3x+2x+6=16$$ Combine like terms: $$5x+6=16$$ Now, isolate $x$ by subtracting 6 from both sides: $$5x=10$$ Finally, divide by 5: $$x=2$$

e) Substitute that value for $x$ into the equation and solve for $y$.

Now substitute $x=2$ back into Equation 2 to find $y$: $$y=x+3=2+3=5$$

f) Use substitution to check your solution for the system.

Now we need to check if our solution $(2,5)$ satisfies both original equations.

Checking in Equation 1: $$3x+2y=16$$ Substituting $x=2$ and $y=5$: $$3(2)+2(5)=6+10=16\text{(True)}$$

Checking in Equation 2: $$y=x+3$$ Substituting $x=2$: $$5=2+3\text{(True)}$$

Since both equations are satisfied, our solution $(x,y)=(2,5)$ is correct.

Final Summary:

• a: $y$
• b: $x+3$
• c: $3x+2(x+3)=16$
• d: $x=2$
• e: $y=5$
• f: Both equations are satisfied, verifying the solution $(2,5)$.