Answer:
(4, -11)
Step-by-step explanation:
We are given the system of equations:
[tex]\displaystyle \begin{cases} 3x+2y=-10\\ y=-5x+9\end{cases}[/tex]
And we want to solve by substitution.
Notice that y is isolated in the second equation.
Therefore, we can substitute the second equation into the first. This gives us:
[tex]3x+2(-5x+9)=-10[/tex]
Now, we can solve for x.
First, distribute:
[tex]\displaystyle 3x-10x+18=-10[/tex]
Next, we can combine like terms:
[tex]-7x+18=-10[/tex]
Subtract 18 from both sides:
[tex]-7x=-28[/tex]
And divide both sides by -7:
[tex]x=4[/tex]
So, the value of x is 4.
Using the second equation then, we can solve for y:
[tex]y=-5x+9[/tex]
Since we know that x = 4:
[tex]\displaystyle y = - 5(4) + 9 = -20 + 9 = -11[/tex]
So, our solution is (4, -11).
To check, we can simply substitute the x and y values and see if the two equations are true.
For the first equation:
[tex]3(4)+2(-11)=12-22=-10\stackrel{\checkmark}{=}-10[/tex]
And for the second equation:
[tex]-5(4)+9=-20+9=-11\stackrel{\checkmark}{=}-11[/tex]
Since both statements are true, (4, -11) is indeed correct!
