Help me to do this problem System by sustitution.
4) y = -3x - 7
-6x - 2y = 14

The system of equations has infinite solutions

Step-by-step explanation:

∵ y = -3x - 7 ⇒ (1)

∵ -6x - 2y = 14 ⇒ (2)

→ Substitute y in equation (2) by equation (1)

∴ -6x - 2(-3x - 7) = 14

→ Simplify the left side

∵ -6x - 2(-3x) - 2(-7) = 14

∴ -6x + 6x + 14 = 14

→ Add the like terms in the left side

∵ (-6x + 6x) + 14 = 14

∴ 0 + 14 = 14

∴ 14 = 14

∵ The variable is disappeared and the two sides of the equation equal

∴ The equation has many solutions

→ That means x and y can be any numbers

∴ The system of equations has infinite solutions

2

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3