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Equation of Family of lines passing through the point of intersection of two lines with examples and animation

SUPPLEMENTARY EXERCISE 10.4 |

**Question 1. **Find the equation of line through the intersection of lines 3*x*+4*y*=7 and *x*–*y*+2=0 and whose slope is 5.

**Question 2. **Find the equation of line through the intersection of lines *c*+2*y*-3=0 and 4*x*–*y*+7=0 and which is parallel to 5*x*+4*y*-20=0

**Question 3. **Find the equation of line through the intersection of lines 2*x*+3*y*-4=0 and *x*-5*y*=7 that has *x*-intercept equal to -4.

**Question 4. **Find the equation of line through the intersection of lines 5*x*-3*y*=1 and 2*x*+3*y*-23=0 and perpendicular to the line 5*x*-3*y*-1=0.