\begin{aligned} x+y&=3 \\\\ x-3y&=-9 \end{aligned} What is the solution (x,y) to the given system of equations?

Align and Add Equations: We have the system of equations: x + y = 3 x - 3y = -9 To solve this system, we can use the method of substitution or elimination. In this case, we will use the elimination method to find the values of 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 coefficient of y in both equations the same (but with opposite signs). 3(x + y) = 3(3) 3x + 3y = 9 Now we have: (3) 3x + 3y = 9 (4) x - 3y = -9Add Equations to Eliminate y: 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: x = 0 / 4 x = 0Solve for x: Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. We will use equation (1): x + y = 3 0 + y = 3 y = 3Substitute x into Equation: We have found the values of x and y: x = 0 y = 3 These values satisfy both original equations, so we have found the solution to the system of equations.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\begin{aligned} x+y&=3, \ & x-3y=-9 \end{aligned}$ $\newline$ What is the solution $(x,y)$ to the given system of equations?

View step-by-step help

Home

Math Problems

Precalculus

Find the magnitude of a three-dimensional vector

Full solution

\begin{aligned} x+y&=3, \ & x-3y=-9 \end{aligned}

\newline

What is the solution

(x,y)

to the given system of equations?

Align and Add Equations: We have the system of equations: $\newline$ $x + y = 3$ $\newline$ $x - 3y = -9$ $\newline$ To solve this system, we can use the method of substitution or elimination. In this case, we will use the elimination method to find the values of $x$ 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 coefficient of $y$ in both equations the same (but with opposite signs). $\newline$ $3(x + y) = 3(3)$ $\newline$ $3x + 3y = 9$ $\newline$ Now we have: $\newline$ $(3) 3x + 3y = 9$ $\newline$ $x + y = 3$ $0$
Add Equations to Eliminate y: 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: $\newline$ $x = 0 / 4$ $\newline$ $x = 0$
Solve for x: Now that we have the value of $x$ , we can substitute it back into one of the original equations to find the value of $y$ . We will use equation ( $1$ ): $x + y = 3$ $0 + y = 3$ $y = 3$
Substitute $x$ into Equation: We have found the values of $x$ and $y$ : $x = 0$ $y = 3$ These values satisfy both original equations, so we have found the solution to the system of equations.