Answer:
The solution to the system of the equations be:
Step-by-step explanation:
Given the system of equations
[tex]2x - 3y = 9[/tex]
[tex]-5x - 3y = 30[/tex]
Solving the system of equations using the elimination method
Multiply [tex]2x-3y=9[/tex] by 5: [tex]10x-15y=45[/tex]
Multiply [tex]-5x-3y=30[/tex] by 2: [tex]-10x-6y=60[/tex]
[tex]\begin{bmatrix}10x-15y=45\\ -10x-6y=60\end{bmatrix}[/tex]
adding the equations
[tex]-10x-6y=60[/tex]
[tex]+[/tex]
[tex]\underline{10x-15y=45}[/tex]
[tex]-21y=105[/tex]
now solving -21y = 105 for y
[tex]-21y=105[/tex]
Divide both sides by -21
[tex]\frac{-21y}{-21}=\frac{105}{-21}[/tex]
Simplify
[tex]y=-5[/tex]
For 10x - 15y = 45 plug in y = -5
[tex]10x-15\left(-5\right)=45[/tex]
Apply the rule -a(-a) = a
[tex]10x+15\cdot \:5=45[/tex]
[tex]10x+75=45[/tex]
Subtract 75 from both sides
[tex]10x+75-75=45-75[/tex]
Simplify
[tex]10x=-30[/tex]
Divide both sides by 10
[tex]\frac{10x}{10}=\frac{-30}{10}[/tex]
Simplify
[tex]x=-3[/tex]
Therefore, the solution to the system of the equations be:
The graph of the solution to the system of equations is also attached below.
