Solve the system of equations by using the substitution method.
3x-5y=14
y=x-4

x = 3

y = -1

(3, -1)

Step-by-step explanation:

Substitute the y variable in 3x-5y=14 with the expression x-4

3x - 5y = 14

3x - 5(x - 4) = 14   Use the distributive property

3x - (5x - 20) = 14   Subtract the binomial

3x - 5x + 20 = 14     Collect like terms

20 - 2x = 14        Isolate "x" now

-2x = 14 - 20      Subtract 20 from both sides

-2x = -6       Divide both sides by -2

x = 3       Solved for x

Substitute x using 3 in one of the equations.

y = x - 4

y = 3 - 4       Subtract

y = -1      Solved for y

The solution as an ordered pair (x, y) is (3, -1).

(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

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