Answer:
From the graph, it is clear that both lines intersect at x=5 and y=-4
Thus, the point of intersection is (x, y) = (5, -4)
(x, y) = (5, -4)
Please check the graph.
Step-by-step explanation:
The solution graph is attached below.
From the attached solution graph,
- The red line is representing the equation 2x+5y=-10
- The blue line is representing the equation y=-3/5x-1
From the graph, it is clear that both lines intersect at x=5 and y=-4
Thus, the point of intersection is (x, y) = (5, -4)
Therefore, the point of intersection is the solution to the system of equations.
Hence, the solution is: (x, y) = (5, -4)
Please check the graph.
LET US SOLVE TO CHECK
[tex]\begin{bmatrix}2x+5y=-10\\ y=-\frac{3}{5}x-1\end{bmatrix}[/tex]
[tex]\mathrm{Arrange\:equation\:variables\:for\:elimination}[/tex]
[tex]\begin{bmatrix}2x+5y=-10\\ \frac{3}{5}x+y=-1\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}2x+5y=-10\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:6x+15y=-30[/tex]
[tex]\mathrm{Multiply\:}\frac{3}{5}x+y=-1\mathrm{\:by\:}10\:\mathrm{:}\:\quad \:6x+10y=-10[/tex]
[tex]\begin{bmatrix}6x+15y=-30\\ 6x+10y=-10\end{bmatrix}[/tex]
[tex]6x+10y=-10[/tex]
[tex]-[/tex]
[tex]\underline{6x+15y=-30}[/tex]
[tex]-5y=20[/tex]
[tex]\begin{bmatrix}6x+15y=-30\\ -5y=20\end{bmatrix}[/tex]
solve for y
[tex]-5y=20[/tex]
Divide both sides by -5
[tex]\frac{-5y}{-5}=\frac{20}{-5}[/tex]
[tex]y=-4[/tex]
[tex]\mathrm{For\:}6x+15y=-30\mathrm{\:plug\:in\:}y=-4[/tex]
[tex]6x+15\left(-4\right)=-30[/tex]
[tex]6x-60=-30[/tex]
[tex]6x=30[/tex]
[tex]x=5[/tex]
Thus, the solution is:
[tex]x=5,\:y=-4[/tex]
