Question

Solve the following system of equations with the substitution method. Write your

answers as an Ordered Pair. If infinitely many solutions exist, enter ∞ (oo). If no
solution exists, enter DNE

System of Equations
y = -2x + 19
y=-13x + 107
Solution:

x+6y=-17
y = -x +3
Solution:

x=8y-51
7x + y = 42
Solution:

x-20y=-25
-x+y=6
Solution:

Answer 1

Let's solve each system of equations using the substitution method:

y = -2x + 19

y = -13x + 107

Since both equations are already solved for y, we can set them equal to each other:

-2x + 19 = -13x + 107

Now, solve for x:

11x = 88

x = 88 / 11

x = 8

Now, substitute the value of x back into one of the original equations to find y:

y = -2(8) + 19

y = 3

Solution: (x, y) = (8, 3)

x + 6y = -17

y = -x + 3

Substitute the value of y from the second equation into the first equation:

x + 6(-x + 3) = -17

Simplify and solve for x:

x - 6x + 18 = -17

-5x + 18 = -17

-5x = -35

x = -35 / -5

x = 7

Now, substitute the value of x back into the second equation to find y:

y = -7 + 3

y = -4

Solution: (x, y) = (7, -4)

x = 8y - 51

7x + y = 42

Substitute the value of x from the first equation into the second equation:

7(8y - 51) + y = 42

Simplify and solve for y:

56y - 357 + y = 42

57y - 357 = 42

57y = 399

y = 399 / 57

y = 7

Now, substitute the value of y back into the first equation to find x:

x = 8(7) - 51

x = 56 - 51

x = 5

Solution: (x, y) = (5, 7)

x - 20y = -25

-x + y = 6

Add the two equations to eliminate x:

(x - 20y) + (-x + y) = -25 + 6

Simplify and solve for y:

-19y = -19

y = -19 / -19

y = 1

Now, substitute the value of y back into one of the original equations to find x:

x - 20(1) = -25

x - 20 = -25

x = -25 + 20

x = -5

Solution: (x, y) = (-5, 1)

So, the solutions to each system of equations are:

(x, y) = (8, 3)

(x, y) = (7, -4)

(x, y) = (5, 7)

(x, y) = (-5, 1)