Answer:
(¹¹⁄₇, -⅐)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}2x+y=3&\\x-3y=2\end{cases}[/tex]
What is the elimination method?
The elimination method is when you rewrite the two equations so that when added together, one of the two variables (x or y) is eliminated.
Step 1: Multiply the first equation by [tex]3[/tex].
[tex]\implies (3)2x+(3)y=(3)3[/tex]
[tex]\implies 6x+3y=9[/tex]
Step 2: Add the above equation to the second equation to eliminate 3y.
[tex]\begin{array}{r l}6x+3y & = 9\\+\ x-3y&=2\\\cline{1-2}7x&=11 \end{array}[/tex]
Step 3: Solve for x (by dividing both sides by 7).
[tex]\implies \dfrac{7x}{7}=\dfrac{11}{7}[/tex]
[tex]\implies \boxed{x=\dfrac{11}{7}}[/tex]
Step 4: Substitute ¹¹⁄₇ as the value of [tex]x[/tex] in any of the given equations and solve for [tex]y[/tex].
[tex]\implies 2\left(\dfrac{11}{7}\right)+y=3[/tex]
[tex]\implies \dfrac{22}{7}+y=3[/tex]
Step 5: Convert [tex]3[/tex] into a fraction and subtract ²²⁄₇ from both sides of the equation.
[tex]\implies \dfrac{22}{7}-\dfrac{22}{7}+y=\dfrac{21}{7}-\dfrac{22}{7}[/tex]
[tex]\implies \boxed{y=-\dfrac{1}{7}}[/tex]
The solution to the given system of equations is (¹¹⁄₇, -⅐).
Learn more here:
brainly.com/question/27868564
