Solve the following system of equations:
y = 4x - 6
5x - 4y = -9

(X=Y)=(3,6)

Step-by-step explanation:

5x-4(4x-6)=-9

x=3

y=4x3-6

y=6

1.

Step 1: Flip the equation.

4x−6=y

Step 2: Add 6 to both sides.

4x−6+6=y+6

4x=y+6

Step 3: Divide both sides by 4.

4x

4

=

y+6

4

x=

1

4

y+

3

2

2.

Step 1: Add 4y to both sides.

5x−4y+4y=−9+4y

5x=4y−9

Step 2: Divide both sides by 5.

5x

5

=

4y−9

5

x=

4

5

y+

−9

5

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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