Question

question 4
which is a correct way to use substitution to solve the system of equations, and what is the solution?
y = -2x
y = 3x + 5
select all that apply:
replace y in equation a with 3x + 5; this gives us 3x + 5 = 2x
replace y in equation b with -2x; this gives us -2x = 3x + 5
solve both equations for x, then set their equivalent terms equal to each other; this gives us \\(\frac{y}{-2} = \frac{y - 5}{3}\\)
(-1, 2)
(1, 3)
(5, -10)
question 5

Explanation:

Step1: Verify substitution method 1

Check first option: Equation A is $y=-2x$. Replacing $y$ with $3x+5$ gives $3x+5=-2x$, not $3x+5=2x$. This is incorrect.

Step2: Verify substitution method 2

Check second option: Equation B is $y=3x+5$. Replacing $y$ with $-2x$ gives $-2x=3x+5$. This is correct.

Step3: Verify substitution method 3

Check third option: Solve $y=-2x$ for $x$: $x=\frac{y}{-2}=-\frac{y}{2}$. Solve $y=3x+5$ for $x$: $3x=y-5$ so $x=\frac{y-5}{3}$. Setting equal gives $-\frac{y}{2}=\frac{y-5}{3}$, not $\frac{y}{2}=\frac{y-5}{3}$. This is incorrect.

Step4: Solve the correct equation

From $-2x=3x+5$, rearrange: $-2x-3x=5$ → $-5x=5$ → $x=-1$. Substitute $x=-1$ into $y=-2x$: $y=-2(-1)=2$. The solution is $(-1,2)$.

Step5: Verify solution options

Check $(-1,2)$: Substitute into $y=3x+5$: $3(-1)+5=-3+5=2=y$. Correct. Check $(1,3)$: $-2(1)=-2≠3$, incorrect. Check $(5,-10)$: $3(5)+5=20≠-10$, incorrect.

Answer:

• Replace y in Equation B with $-2x$; this gives us $-2x = 3x + 5$
• $(-1,2)$