Graph & Check to solve linear system?

Question

 

(1   y=-x+3, y=x+1    (2   y=-3, x=3   (3   y=2x-4, y= -1 pver 2x +1   (4  y=-x+5, y=x+1   (5  2x-y=2   (6  y= -2x +2, x-y=4  (7  2x-3y=9, x= -3   (8 -x+y=1, 2x+y= -2 (SKIP #9) (10  7y= -14x+42, 7y=14x+14 THANKS please show GRAPH?? & all work thank you ;)

Answer 1

All the equations have been plotted on the same graph, but colour-coding has been used to make it easier to identify the intersections (where applicable) and hence the solutions.

(1) Add the equations: 2y=4, y=2, so x=1. See Q1(1,2) in orange.

(2) See Q2(3,-3) in red.

(3) 2x-4=-1/(2x+1), (2x-4)(2x+1)+1=0, 4x²-6x-3=0, x=(6±√(36+48))/8=(6±√84)/8=(3±√21)/4=0.75±1.1456.

x=1.8956, y=-0.2087; x=-0.3956, y=-4.7913. See Q3.1 and Q3.2 (blue). This is the only curve involved in your question.

(4) Add the equations: 2y=6, y=3, so x=2. See Q4 (orange).

(5) Black line implies many solutions.

(6) x-y=4, y=x-4; y=-2x+2, so x-4=-2x+2, 3x=6, x=2, y=x-4=-2. See Q6 (purple).

(7) 2x-3y=9, so -6-3y=9, 3y=-15, y=-5, 2x+15=9, 2x=-6, x=-3. See Q7 (orange).

(8) -x+y=1, 2x+y=-2. Subtract first eqn from second: 3x=-3, x=-1 so y=0. See Q8 (orange).

(10) Divide both eqns by 7: y=-2x+6, y=2x+2, so -2x+6=2x+2, 4=4x, x=1, y=4. See Q10 (green).