Answer:
x = -1, y = -6
Step-by-step explanation:
[tex]$A system of equations, also known as a set of simultaneous equations can be solved using several commonly used methods.$[/tex]
[tex]\text{Let} \\ \\y \ = \ 6x \quad $-----$ \; (1) \\ \\2x \ + \ 3y \ = \ -20 \quad $-----$ \; (2). \\ \\ \\ 1. \quad \text{The Substitution Method} \\ \\\\\text{Substitute equation (1) into equation (2), yielding} \\ \\\\2x \ + \ 3(6x) \ = \ -20 \\ \\2x \ + \ 18x \ = \ -20 \\ \\20x \ = \ -20 \\ \\x \ = \ -1 \\ \\\text{Since} \ \ x \ = -1, \text{using equation (1) to find the value of } y, \\ \\y \ = \ 6 (-1) \\ \\y \ = \ -6[/tex]
[tex]2. \quad \text{The Elimination Method} \\ \\ \text{First, multiply each term of equation (1) by 3, giving} \\ \\ y \ \times \ 3 \ = \ (6x) \ \times \ 3 \\ \\ 3y \ = \ 18x \\ \\ \text{Rearrange the equation such that the one side of the previous equation becomes 0.} \\ \\ 18x \ - \ 3y \ = \ 0 \qquad $-----$ \; (3) \\ \\ \text{Add equation (2) and equation (3) together,} \\ \\ (2x \ + \ 3y) + (18x \ - \ 3y) \ = \ -20 + 0 \\ \\ 2x \ + \ 18x \ + \ 3y \ - \ 3y \ = \ -20 \\ \\ 20x \ = \ -20 \\ \\ x \ = \ -1[/tex]
[tex]\text{When} \ \ x \ = \ -1, \ \ \text{according to equation (1),} \\ \\ y \ = \ 6(-1) \\ \\ y \ = \ -6[/tex]
