Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=1[/tex]
Step-by-step explanation:
Given the equations
[tex]-5x-18y=-28[/tex]
[tex]-10x+9y=-11[/tex]
solving the system of the equation by elimination method
[tex]\begin{bmatrix}-5x-18y=-28\\ -10x+9y=-11\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-5x-18y=-28\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-10x-36y=-56[/tex]
[tex]\begin{bmatrix}-10x-36y=-56\\ -10x+9y=-11\end{bmatrix}[/tex]
[tex]-10x+9y=-11[/tex]
[tex]-[/tex]
[tex]\underline{-10x-36y=-56}[/tex]
[tex]45y=45[/tex]
[tex]\begin{bmatrix}-10x-36y=-56\\ 45y=45\end{bmatrix}[/tex]
solve 45y=5 for y:
[tex]45y=45[/tex]
[tex]\frac{45y}{45}=\frac{45}{45}[/tex]
[tex]y=1[/tex]
[tex]\mathrm{For\:}-10x-36y=-56\mathrm{\:plug\:in\:}y=1[/tex]
solve [tex]-10x-36\cdot \:1=-56[/tex] for x:
[tex]-10x-36\cdot \:1=-56[/tex]
[tex]-10x-36=-56[/tex]
Add 36 to both sides
[tex]-10x-36+36=-56+36[/tex]
[tex]-10x=-20[/tex]
[tex]\frac{-10x}{-10}=\frac{-20}{-10}[/tex]
[tex]x=2[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
