Question

each statement represents the last line after substituting one equation of a system of linear equations into the other equation. match each statement to the type of solution for the system.
no solution
select
infinitely many solutions
select
one solution
select
solve the system of linear equations using substitution.
$3a + 4b = 28$
$5a - 4b = -12$
$(-2, -11/2)$
$(2, 11/2)$
$(11/2, 2)$
solve the system of linear equations using substitution.

Explanation:

Step1: Isolate a variable from Eq1

From $3a + 4b = 28$, solve for $4b$:
$4b = 28 - 3a$

Step2: Substitute into Eq2

Replace $4b$ in $5a - 4b = -12$:
$5a - (28 - 3a) = -12$

Step3: Simplify and solve for $a$

Expand and combine like terms:
$5a - 28 + 3a = -12$
$8a = 16$
$a = 2$

Step4: Find $b$ using $a=2$

Substitute $a=2$ into $4b = 28 - 3a$:
$4b = 28 - 3(2) = 22$
$b = \frac{22}{4} = \frac{11}{2}$

• No Solution: Matches a false numerical statement (e.g., $0=5$) after substitution, meaning parallel lines.
• Infinitely Many Solutions: Matches a true numerical statement (e.g., $0=0$) after substitution, meaning coinciding lines.
• One Solution: Matches a statement that solves for a single variable value (e.g., $x=3$) after substitution, meaning intersecting lines.

Answer:

B. (2, 11/2)

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