Question

3x-4y=-5

y=4x-2

is (1,2) a solution of the system?

Answer 1

Yes it’s a solution

`\Large\texttt{Explanation}`

In order to find out whether or not a point is a solution to a system of equations, we need to plug in each of the coordinates into each of the equations in the system. If the point really is a solution, then it makes both equations true.

Given System:

3x - 4y = -5

y = 4x - 2

Given Point:

(1,2)

So the way we do this is we plug in 1 for x, and 2 for y:

3(1) - 4(2) = -5

2 = 4(1) - 2

Now simplify:

3 - 8 = -5

2 = 4 - 2

Simplify further:

-5 = -5

2 = 2

The point (1,2) IS a solution to this system, because it makes both equations true.

`\therefore` (1,2) is a solution

Answer 2

Yes, (1, 2) is a solution to the given system of equations.

Explanation:

Given system of equations:

`\begin{cases}3x-4y=-5\\y=4x-2\end{cases}`

To determine if the point (1, 2) is a solution to the given system of equations, we can substitute the values x = 1 and y = 2 into both equations then check if the left side of each equation is equal to the right side.

Equation 1: 3x - 4y = -5

Substitute x = 1 and y = 2 into equation 1:

`\begin{aligned}3(1) - 4(2) &\overset{?}{=} -5\\\\3 - 8 &\overset{?}{=} -5\\\\-5&\overset{\checkmark}{=} -5\end{aligned}`

As the left side is equal to the right side then (1, 2) satisfies the first equation.

Equation 2: y = 4x - 2

Substitute x = 1 and y = 2 into equation 2:

`\begin{aligned}2 &\overset{?}{=} 4(1)-2\\\\2 &\overset{?}{=}4-2\\\\2&\overset{\checkmark}{=} 2\end{aligned}`

The left side is equal to the right side (2), so (1, 2) satisfies the second equation.

Conclusion

Since (1, 2) satisfies both equations, it is indeed a solution to the system.