Question

Lines C and D are represented by the equations given below:

Line C: y=x+8
Line D: y=3x+2

Which statement shows the solution to the system of equations given below:
(3, 11) because the point does not lie on any axis
(3, 11) because both lines pass through this point
(4, 14) because one of the lines passes through this point
(4, 14) because the point lies between the two axes

Answer 1

The answer is (3,11) because both lines pass through this point.

If you plug these coordinates into the equations in place of x and y :

3+8= 11

3(3)+2= 11

So we know that the coordinates (3,11) are correct, however the answer is C. because solutions to systems of equations are represented by a point of intersection.

Answer 2

Hello!

The answer is:

The correct option is the second option:

(3, 11) because both lines pass through this point

Why?

To find which statement shows the solution to the system of equations, we need to find which of the given points are solutions to the system of equations. We must remember that if a point is a solution to a system of equations, it will satisfy both equations.

So, we are given the lines:

Line C

`y=x+8`

Line D

`y=3x+2`

Now, evaluating the first point to see if satisfies the line equations:

Evaluating (3,11)

Line C

`11=3+8`

`11=11`

We have that the point (3,11) satisfy the equation of the Line C, so, the linea pass through this point.

Line D

`y=3x+2`

`11=3*3+2`

`11=11`

We have that the point (3,11) satisfies the equation of the Line C, so, the linea pass through this point.

Hence, we have that the points satisfies both lines, so it's a solution to the system of equation.

So, the correct option is the second option:

(3, 11) because both lines pass through this point

Have a nice day!