Question

#1: Solve the linear system below using the elimination method. Type your

answer as an ordered pair in the form (#,#).*
2x + 5y = -16
-3x + 7y = -5

Answer 1

`(-3,-2)`

Explanation:

First, you need to get one like term in each equation the same in order to eliminate. To do less damage to the equation, we'll use the x terms.

To get the x terms the same, multiply both equations by the opposite x term:

`-3(2x+5y)=-3(-16)\\\\2(-3x+7y)=2(-5)`

Simplify by multiplying. Use the distributive property for the left side (remember, two negatives make a positive and a negative multiplied by a positive will always be negative):

`-3(2x)-3(5y)=-3(-16)\\\\2(-3x)+2(7y)=2(-15)\\\\\\-6x-15y=48\\\\-6x+14y=-10`

Now subtract all like terms. The x terms cancel out:

`-6x-(-6x)=0\\\\-15y-14y=-29y\\\\48-(-10)=58\\\\-29y=58`

Now solve the new equation for y. Isolate the variable by using inverse operations. The term can be seen as -29×y. In order to isolate the variable, use division (opposite of multiplication). Divide both sides by 29:

`(-29y)/(29) =(58)/(29) \\\\-1y=2`

Make the variable positive. Multiply both sides by -1:

`-1(-1y)=-1(2)\\\\y=-2`

The value of y is -2. Insert this value into either original equation:

`2x+5(-2)=-16`

Solve for x. Simplify multiplication:

`2x-10=-16`

Use inverse operations to get like terms on the same side of the equation. Add 10 to both sides (addition is the opposite of subtraction) to cancel out the -10 on the left:

`2x-10+10=-16+10\\\\2x=-6`

Isolate the variable using inverse operations. The x term can be seen as 2×x. Division is the opposite of multiplication, so divide both sides by 2:

`(2x)/(2)=(-6)/(2) \\\\x=-3`

The value of x is -3. Therefore, the solution to the system is:

`(-3_(x),-2_(y))`

:Done