Question

Sketch a system of two linear equations whose solution is (-1,3).

Answer 1

Answer:

The two equations are  y=x+4 and y=2x+5.

Step-by-step explanation:

Given that (-1,3) is solutions of the system of two linear equations.

Let y=mx + c be the generalized equation of line having slope m and y-intercept c.

For different values of m and c, there are corresponding linear equations.

As the lines are passing through the point (-1,3), so, pot x=-1 and y=3 in the generalized equation, we have

$3=-1m+c \\\\\Rightarrow 3=-m+c \\\\\Rightarrow c-m=3\cdots(i).$

All the real values of c and m which satisfy equation (i) are the desired linear equations.

As we required only two linear equations, take any two values of c and m.

For c=4 and m=1 (satisfying equation (i))

$y=1\times x +4 \\\\\Rightarrow y=x+4$

and for c=5, m=2

$y=2\times x +5 \\\\\Rightarrow y=2x+5.$

Hence, the two equations are  y=x+4 and y=2x+5.