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).](https://tex.z-dn.net/?f=3%3D-1m%2Bc%20%5C%5C%5C%5C%5CRightarrow%203%3D-m%2Bc%20%5C%5C%5C%5C%5CRightarrow%20c-m%3D3%5Ccdots%28i%29.)
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](https://tex.z-dn.net/?f=y%3D1%5Ctimes%20x%20%2B4%20%5C%5C%5C%5C%5CRightarrow%20y%3Dx%2B4)
and for c=5, m=2
![y=2\times x +5 \\\\\Rightarrow y=2x+5.](https://tex.z-dn.net/?f=y%3D2%5Ctimes%20x%20%2B5%20%5C%5C%5C%5C%5CRightarrow%20y%3D2x%2B5.)
Hence, the two equations are y=x+4 and y=2x+5.
Answer:
2/3
Step-by-step explanation:
Distance MS = √[(6-(-3))²+(3-3)²]= 9
Distance M'S' = √[(4-(-2))²+(2-2)²] =6
scale factor = |M'S'| /|MS|= 6/9 = 2/3