Question

PART 2...Solve the below system of equations using the best method. Please describe the method used [substitution, graphing, elimination, etc], and give your answer in the form (x,y).

1.) 7x + 2y = 4
y = -4x + 1


2.) 3x - 4y = 1
-2x + 3y = 1

Answer 1

1.) The second equation is already solved for y, so this system can be solved with substitution.

7x + 2y = 4
y = -4x + 1

Substitute what y is equal to from the second equation into y of the first equation.

7x + 2(-4x + 1) = 4

7x - 8x + 2 = 4

-x + 2 = 4

-x = 2

x = -2

Now substitute x with -2 in the second original equation to find y.

y = -4x + 1

y = -4(-2) + 1

y = 8 + 1

y = 9

Solution: (-2, 9)

2.) The first equation has 3x. The second equation has -2x. Multiply the first equation by 2 and the second equation by 3 and add them to use the elimination method.

3x - 4y = 1
-2x + 3y = 1

6x - 8y = 2
-6x + 9y = 3
-----------------
y = 5

The first original equation has -4y, and the second original equation has 3y. Multiply the first equation by 3 and teh second by 4 and add them to eliminate y.

9x - 12y = 3
-8x + 12y = 4
------------------
x = 7

Solution: (7, 5)