x+y=3 x-3y=-9 What is the solution (x,y) to the given system of equations? Choose 1 answer: (A) (-3,0) (B) (0,3) (C) (1,2) (D) (9,-6)

Align and Add Equations: We have the system of equations: x + y = 3 x - 3y = -9 Let's solve this system using the method of substitution or elimination. We will use the elimination method to solve for x and y.Multiply and Eliminate y: First, we will align the equations and add them together to eliminate y: (1) x + y = 3 (2) x - 3y = -9 We will multiply equation (1) by 3 to make the coefficients of y in both equations equal but opposite in sign: 3(x + y) = 3(3) 3x + 3y = 9 Now we have: (3) 3x + 3y = 9 (4) x - 3y = -9Add Equations to Solve: Next, we add equations (3) and (4) together: (3x + 3y) + (x - 3y) = 9 + (-9) 3x + x + 3y - 3y = 0 4x = 0 Now we can solve for x: 4x = 0 x = 0 / 4 x = 0Substitute x to Find y: Now that we have the value of x, we can substitute it back into one of the original equations to find y. We'll use equation (1): x + y = 3 0 + y = 3 y = 3Final Solution: We have found the values of x and y: x = 0 y = 3 The solution to the system of equations is (x, y) = (0, 3).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$x+y=3$ $\newline$ $x-3y=-9$ $\newline$ What is the solution $(x,y)$ to the given system of equations? $\newline$ Choose $1$ answer: $\newline$ (A) $(-3,0)$ $\newline$ (B) $(0,3)$ $\newline$ (C) $(1,2)$ $\newline$ (D) $(9,-6)$

View step-by-step help

Home

Math Problems

Algebra 2

Write a quadratic function from its x-intercepts and another point

Full solution

x+y=3

\newline

x-3y=-9

\newline

What is the solution

(x,y)

to the given system of equations?

\newline

Choose

1

answer:

\newline

(A)

(-3,0)

\newline

(B)

(0,3)

\newline

(C)

(1,2)

\newline

(D)

(9,-6)

Align and Add Equations: We have the system of equations: $\newline$ $x + y = 3$ $\newline$ $x - 3y = -9$ $\newline$ Let's solve this system using the method of substitution or elimination. We will use the elimination method to solve for $x$ and $y$ .
Multiply and Eliminate y: First, we will align the equations and add them together to eliminate y: $\newline$ $(1)\ x + y = 3$ $\newline$ $(2)\ x - 3y = -9$ $\newline$ We will multiply equation $(1)$ by $3$ to make the coefficients of y in both equations equal but opposite in sign: $\newline$ $3(x + y) = 3(3)$ $\newline$ $3x + 3y = 9$ $\newline$ Now we have: $\newline$ $(3)\ 3x + 3y = 9$ $\newline$ $(4)\ x - 3y = -9$
Add Equations to Solve: Next, we add equations ( $3$ ) and ( $4$ ) together: $\newline$ $(3x + 3y) + (x - 3y) = 9 + (-9)$ $\newline$ $3x + x + 3y - 3y = 0$ $\newline$ $4x = 0$ $\newline$ Now we can solve for x: $\newline$ $4x = 0$ $\newline$ $x = 0 / 4$ $\newline$ $x = 0$
Substitute $x$ to Find $y$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to find $y$ . We'll use equation ( $1$ ): $x + y = 3$ $0 + y = 3$ $y = 3$
Final Solution: We have found the values of $x$ and $y$ : $x = 0$ $y = 3$ The solution to the system of equations is $(x, y) = (0, 3)$ .