Solve using augmented matrices. 4x − 6y = –12 y = –4 (_____, _____)

Write Augmented Matrix: First, let's write the system of equations as an augmented matrix. We have: 4x - 6y = -12 y = -4 So the augmented matrix is: [4 -6 | -12] [0 1 | -4]Substitute y in First Equation: Since the second equation is already solved for y, we can use it to substitute y in the first equation. Substitute y = -4 into the first equation: 4x - 6(-4) = -12 4x + 24 = -12Solve for x: Now, let's solve for x. Subtract 24 from both sides: 4x = -12 - 24 4x = -36Find x: Divide both sides by 4 to find x: x = -36 / 4 x = -9Final Solution: We already have y from the second equation, y = -4. So the solution to the system of equations is: x = -9, y = -4

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using augmented matrices. $\newline$ $4x - 6y = -12$ $\newline$ $y = -4$ $\newline$ (_, _)

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using any method

Full solution

Q. Solve using augmented matrices.

\newline

4x - 6y = -12

\newline

y = -4

\newline

(_____, _____)

Write Augmented Matrix: First, let's write the system of equations as an augmented matrix. $\newline$ We have: $\newline$ $4x - 6y = -12$ $\newline$ $y = -4$ $\newline$ So the augmented matrix is: $\newline$ \begin{bmatrix}4 & -6 & | & -12\0 & 1 & | & -4\end{bmatrix}
Substitute $y$ in First Equation: Since the second equation is already solved for $y$ , we can use it to substitute $y$ in the first equation. $\newline$ Substitute $y = -4$ into the first equation: $\newline$ $4x - 6(-4) = -12$ $\newline$ $4x + 24 = -12$
Solve for x: Now, let's solve for $x$ . $\newline$ Subtract $24$ from both sides: $\newline$ $4x = -12 - 24$ $\newline$ $4x = -36$
Find $x$ : Divide both sides by $4$ to find $x$ :
$x = \frac{-36}{4}$
$x = -9$
Final Solution: We already have $y$ from the second equation, $y = -4$ . $\newline$ So the solution to the system of equations is: $\newline$ $x = -9$ , $y = -4$