# Solve the matrix equation: 4[2x,y,3z]+3[2,−4,6]=[20,−4,54]

Question
Systems of equations
Solve the matrix equation: $$\displaystyle{4}{\left[{2}{x},{y},{3}{z}\right]}+{3}{\left[{2},−{4},{6}\right]}={\left[{20},−{4},{54}\right]}$$

2021-01-03
Solving this system means solving each of the following equations: $$\displaystyle{8}{x}+{6}={20},$$
$$\displaystyle{4}{y}−{12}=−{4},$$
and
$$\displaystyle{12}{z}+{18}={54}$$
You can obtain these equations by performing scalar multiplication on the vectors given. From here, you just use basic algebra to find that the solutions are as follows:
$$\displaystyle{x}={\frac{{{14}{\left\lbrace{8}\right\rbrace},{y}={2},{\quad\text{and}\quad}{z}={3}.}}{}}$$

### Relevant Questions

Solve the matrix equation: $$4[2x,y,3z]+3[2,−4,6]=[20,−4,54]$$
a) Convert the following equations into matrix:
$$\displaystyle{x}–{y}={3}$$
$$\displaystyle{2}{x}+{3}{y}={1}$$
What is the solution of the system of equations?
y = 2x - 3
5x + y = 11
A (2, 1)
B (1, 2)
C (3, -4)
D (1, -1)
Solve the system: {(-3x,+,y,=,2),(9x,-,3y,=,-6):}
x-y+2x=3
2x+z=1
3x+2y+z=4