Answer:
One solution: (-1, 3)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x-7y=-22\\4x-2y=-10\end{cases}[/tex]
To solve the system of equations by the method of substitution, begin by rearranging the first equation to isolate x:
[tex]x-7y=-22\\\\x-7y+7y=-22+7y\\\\x=7y-22[/tex]
Now, substitute x = 7y - 22 into the second equation and solve for y:
[tex]4(7y-22)-2y=-10\\\\28y-88-2y=-10\\\\26y-88=-10\\\\26y-88+88=-10+88\\\\26y=78\\\\\dfrac{26y}{26}=\dfrac{78}{26}\\\\y=3[/tex]
Therefore, the value of y is y = 3.
Substitute y = 3 into x = 7y - 22 to find the value of x:
[tex]x=7(3)-22\\\\x=21-22\\\\x=-1[/tex]
Therefore, the value of x is x = -1.
So, there is one solution to the given system of equations, which is:
[tex]\LARGE\boxed{\boxed{(-1, 3)}}[/tex]
