6(y-4)=x-3 y=C In the system of equations, C is a constant. For which value of C is (x,y)=(-3,3) a solution? Choose 1 answer: (A) 3 (B) 21 (C) All real numbers (D) None of the above

Substitute y = C: Substitute y = C into the equation 6(y-4) = x-3. Since y = C, the equation becomes 6(C-4) = x-3. Plug in values: Plug in the values x = -3 and y = 3 from the solution point (-3,3) into the equation. This gives us 6(3-4) = -3 - 3. Simplify left side: Simplify the left side: 6(-1) = -6. Now, the equation is -6 = -6. Check against original substitution: Since the equation -6 = -6 holds true, the value of C that makes (x,y) = (-3,3) a solution must be checked against the original substitution. We substituted y = C, and since y = 3 in the solution point, C must be 3.

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6(y-4)=x-3

y=C
In the system of equations,
C is a constant. For which value of
C is
(x,y)=(-3,3) a solution?
Choose 1 answer:
(A) 3
(B) 21
(C) All real numbers
(D) None of the above

$6(y-4)=x-3$ $\newline$ $y=C$ $\newline$ In the system of equations, $C$ is a constant. For which value of $C$ is $(x, y)=(-3,3)$ a solution? $\newline$ Choose $1$ answer: $\newline$ (A) $3$ $\newline$ (B) $21$ $\newline$ (C) All real numbers $\newline$ (D) None of the above

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Math Problems

Algebra 2

Find the number of solutions to a system of equations

Full solution

6(y-4)=x-3

\newline

y=C

\newline

In the system of equations,

C

is a constant. For which value of

C

(x, y)=(-3,3)

a solution?

\newline

Choose

1

answer:

\newline

(A)

3

\newline

(B)

21

\newline

\newline

(D) None of the above

Substitute $y = C$ : Substitute $y = C$ into the equation $6(y-4) = x-3$ . Since $y = C$ , the equation becomes $6(C-4) = x-3$ .
Plug in values: Plug in the values $x = -3$ and $y = 3$ from the solution point $(-3,3)$ into the equation. This gives us $6(3-4) = -3 - 3$ .
Simplify left side: Simplify the left side: $6(-1) = -6$ . Now, the equation is $-6 = -6$ .
Check against original substitution: Since the equation $-6 = -6$ holds true, the value of $C$ that makes $(x,y) = (-3,3)$ a solution must be checked against the original substitution. We substituted $y = C$ , and since $y = 3$ in the solution point, $C$ must be $3$ .