which ordered pair is a solution of the equation? -3x+5y=2x+3y Choose 1 answer: (A) Only (2,4) (B) Only (3,3) (C) Both (2,4) and (3,3) (D) Neither

Combine like terms: Simplify the equation by combining like terms. We want to get all the x terms on one side and all the y terms on the other side. -3x + 5y = 2x + 3y Add 3x to both sides to move the x terms to one side: -3x + 3x + 5y = 2x + 3x + 3y This simplifies to: 5y = 5x + 3yMove x terms: Subtract 3y from both sides to isolate the y terms. 5y - 3y = 5x + 3y - 3y This simplifies to: 2y = 5xIsolate y terms: Divide both sides by 2 to solve for y in terms of x. 2y / 2 = 5x / 2 This simplifies to: y = (5/2)xSolve for y: Test the ordered pairs to see which one(s) satisfy the equation y = (5/2)x. For (A) (2,4), substitute x = 2 and y = 4 into the equation: 4 = (5/2)(2) 4 = 5 This is not true, so (2,4) is not a solution.Test (2,4): Test the ordered pair (B) (3,3). Substitute x = 3 and y = 3 into the equation: 3 = (5/2)(3) 3 = 15/2 This is not true, so (3,3) is not a solution.Test (3,3): Since neither (A) (2,4) nor (B) (3,3) satisfy the equation y = (5/2)x, the correct answer is (D) Neither.

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which ordered pair is a solution of the equation? $\newline$ $-3x+5y=2x+3y$ $\newline$ Choose $1$ answer: $\newline$ (A) Only $(2,4)$ $\newline$ (B) Only $(3,3)$ $\newline$ (C) Both $(2,4)$ and $(3,3)$ $\newline$ (D) Neither

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Algebra 1

Create linear equations with no solutions or infinitely many solutions

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Q. which ordered pair is a solution of the equation?

\newline

-3x+5y=2x+3y

\newline

Choose

1

answer:

\newline

(A) Only

(2,4)

\newline

(B) Only

(3,3)

\newline

(2,4)

and

(3,3)

\newline

(D) Neither

Combine like terms: Simplify the equation by combining like terms. $\newline$ We want to get all the $x$ terms on one side and all the $y$ terms on the other side. $\newline$ $-3x + 5y = 2x + 3y$ $\newline$ Add $3x$ to both sides to move the $x$ terms to one side: $\newline$ $-3x + 3x + 5y = 2x + 3x + 3y$ $\newline$ This simplifies to: $\newline$ $5y = 5x + 3y$
Move x terms: Subtract $3y$ from both sides to isolate the y terms. $\newline$ $5y - 3y = 5x + 3y - 3y$ $\newline$ This simplifies to: $\newline$ $2y = 5x$
Isolate y terms: Divide both sides by $2$ to solve for $y$ in terms of $x$ . $\frac{2y}{2} = \frac{5x}{2}$ This simplifies to: $y = \left(\frac{5}{2}\right)x$
Solve for $y$ : Test the ordered pairs to see which one(s) satisfy the equation $y = \frac{5}{2}x$ . For (A) $(2,4)$ , substitute $x = 2$ and $y = 4$ into the equation: $4 = \frac{5}{2}(2)$ $4 = 5$ This is not true, so $(2,4)$ is not a solution.
Test $2,4$ : Test the ordered pair $B$ $3,3$ . $\newline$ Substitute $x = 3$ and $y = 3$ into the equation: $\newline$ $3 = \left(\frac{5}{2}\right)(3)$ $\newline$ $3 = \frac{15}{2}$ $\newline$ This is not true, so $3,3$ is not a solution.
Test $3,3$ : Since neither (A) $2,4$ nor (B) $3,3$ satisfy the equation $y = \frac{5}{2}x$ , the correct answer is (D) Neither.