Answer:
x = -2, y = 1
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=2x+5\\y=-3x-5 \end{cases}[/tex]
Solve by Substitution
Substitute the first equation into the second equation and solve for x:
[tex]\implies 2x+5=-3x-5[/tex]
Add 3x to both sides:
[tex]\implies 2x+5+3x=-3x-5+3x[/tex]
[tex]\implies 5x+5=-5[/tex]
Subtract 5 from both sides:
[tex]\implies 5x+5-5=-5-5[/tex]
[tex]\implies 5x=-10[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{5x}{5}=\dfrac{-10}{5}[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies y=2(-2)+5[/tex]
[tex]\implies y=-4+5[/tex]
[tex]\implies y=1[/tex]
Therefore, the solution to the given system of equations is (-2, 1).
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