Question

Carlos solved a system of linear equations. He found that exactly one point satisfied both equations. What do you know for certain is true about the two lines

Answer 1

Answer:The two lines intersect (in other words, they have a common meeting points)

Step-by-step explanation:Step-by-step explanation:

Thinking process:

A linear equation takes the form of

where , m = gradient

c = y-intercept (point where the line cuts the y-axis)\

Suppose we have these two linear equations:

We can find the point of intersection by solving the two equations simultaneously like this:

sub y = 2x + 4 into equation (2) gives:

2(2x+4) = -6x -1

solving yields - 0.9

Substituting x= -0.9 into equation 1 yields:

y = 2.2

In terms of the Cartesian coordinates (x, y) the point of intersection will be (-0.9, 2.2)

Hence, the point of intersection is a solution of two linear equations.

Answer 2

The two lines intersect (in other words, they have a common meeting points)

Explanation:

Thinking process:

A linear equation takes the form of
`y = mx + c`

where , m = gradient

c = y-intercept (point where the line cuts the y-axis)\

Suppose we have these two linear equations:
`y = 2x + 4\\ 2y = -6x -1`

We can find the point of intersection by solving the two equations simultaneously like this:

sub y = 2x + 4 into equation (2) gives:

2(2x+4) = -6x -1

solving yields
`x=` - 0.9

Substituting x= -0.9 into equation 1 yields:

`y = 2 (-0.9) + 4\\ = -1.8 + 4\\ = 2.2`

y = 2.2

In terms of the Cartesian coordinates (x, y) the point of intersection will be (-0.9, 2.2)

Hence, the point of intersection is a solution of two linear equations.