Question

Solving systems elimination: I don’t understand how to solve at all. Please help if you can.

Answer 1

The solution to given system of equations y = 3x - 9 and y = -2x + 16 are (x, y) = (5, 6)

The solution to given system of equations y = 5x + 22 and -6x - 4y = -10 are (x, y) = (-3, 7)

Solution:

Given that, we have to solve each system by substitution method

Given system of equations are:

y = 3x - 9 ----------- eqn 1

y = -2x + 16 -------- eqn 2

Substitution method is done by substituting eqn 2 in eqn 1

Substitute the value of "y" from eqn 2 into eqn 1

-2x + 16 = 3x - 9

Move the variables to one side and constants to other side

-2x - 3x = -9 - 16

Combine the like terms

-5x = -25

Cancel the negative sign on both sides of equation

5x = 25

$x = \frac{25}{5} = 5$

x = 5

Substitute x = 5 in eqn 1

y = 3(5) - 9

y = 15 - 9

y = 6

Thus solution to given system of equations are (x, y) = (5, 6)

Given another system of equations are:

y = 5x + 22 ----- eqn 1

-6x - 4y = -10 ------ eqn 2

Substitute eqn 1 in eqn 2

-6x - 4(5x + 22) = -10

-6x - 20x - 88 = -10

Move the variables to one side and constants to other side

-26x = -10 + 88

-26x = 78

x = -3

Substitute x = -3 in eqn 1

y = 5( - 3) + 22

y = -15 + 22

y = 7

Thus solution to given system of equations are (x, y) = (-3, 7)