Solve using augmented matrices. x = 7 3x + 3y = 18 (_____, _____)

Write Equations in Matrix Form: First, let's write the system of equations in matrix form. We have x = 7 and 3x + 3y = 18. The augmented matrix is: [1 0 | 7] [3 3 | 18]Eliminate X-Term: Now, we need to use the first equation to eliminate the x-term from the second equation in the matrix. We can multiply the first row by -3 and add it to the second row. -3 * [1 0 | 7] = [-3 0 | -21] Adding this to the second row: [3 3 | 18] + [-3 0 | -21] = [0 3 | -3]Solve for Y: The new matrix is: [1 0 | 7] [0 3 | -3] Now we can solve for y by dividing the second row by 3. [0 3 | -3] ÷ 3 = [0 1 | -1]Final Matrix: The final matrix is: [1 0 | 7] [0 1 | -1] This tells us that x = 7 and y = -1.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using augmented matrices. $\newline$ $x = 7$ $\newline$ $3x + 3y = 18$ $\newline$ (_, _)

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using elimination

Full solution

Q. Solve using augmented matrices.

\newline

x = 7

\newline

3x + 3y = 18

\newline

(_____, _____)

Write Equations in Matrix Form: First, let's write the system of equations in matrix form. We have $x = 7$ and $3x + 3y = 18$ . The augmented matrix is: $\begin{matrix} 1 & 0 & | & 7 \ 3 & 3 & | & 18 \end{matrix}$
Eliminate X-Term: Now, we need to use the first equation to eliminate the $x$ -term from the second equation in the matrix. $\newline$ We can multiply the first row by $-3$ and add it to the second row. $\newline$ $-3 \times [1 0 | 7] = [-3 0 | -21]$ $\newline$ Adding this to the second row: $\newline$ $[3 3 | 18] + [-3 0 | -21] = [0 3 | -3]$
Solve for Y: The new matrix is: $\newline$ $\begin{matrix} 1 & 0 & | & 7 \ 0 & 3 & | & -3 \end{matrix}$ $\newline$ Now we can solve for $y$ by dividing the second row by $3$ . $\newline$ $\begin{matrix} 0 & 3 & | & -3 \end{matrix}$ $\div 3 = \begin{matrix} 0 & 1 & | & -1 \end{matrix}$
Final Matrix: The final matrix is: $\newline$ \begin{array}{cc|c} 1 & 0 & 7 \ 0 & 1 & -1 \end{array} $\newline$ This tells us that $x = 7$ and $y = -1$ .