Question

solve the following system using elimination by adding. enter your answers by filling in the blanks of the ordered pair.
$-6x + 5y = 1$
$6x + 4y = -10$
( type your answer_, type your answer_)
2 fill in the blank 1 point
solve the following system using elimination by subtracting. enter your answer by filling in the blanks of the ordered pair.
$x + 4y = -3$
$x + 7y = -12$
( type your answer_, type your answer_)

Explanation:

First System (Elimination by Adding)

Step1: Add the two equations

We have the system:

$$\begin{cases}-6x + 5y = 1\\6x + 4y = -10\end{cases}$$

Adding the two equations together: $(-6x + 5y)+(6x + 4y)=1+(-10)$
Simplify the left side: $-6x + 6x+5y + 4y = 9y$
Simplify the right side: $1 - 10=-9$
So we get $9y=-9$

Step2: Solve for y

Divide both sides of $9y = -9$ by 9: $y=\frac{-9}{9}=-1$

Step3: Substitute y into one equation to find x

Substitute $y = -1$ into the second equation $6x + 4y=-10$:
$6x+4\times(-1)=-10$
Simplify: $6x-4=-10$
Add 4 to both sides: $6x=-10 + 4=-6$
Divide both sides by 6: $x=\frac{-6}{6}=-1$

Second System (Elimination by Subtracting)

Step1: Subtract the two equations

We have the system:

$$\begin{cases}x + 4y=-3\\x + 7y=-12\end{cases}$$

Subtract the first equation from the second equation: $(x + 7y)-(x + 4y)=-12-(-3)$
Simplify the left side: $x - x+7y - 4y = 3y$
Simplify the right side: $-12 + 3=-9$
So we get $3y=-9$

Step2: Solve for y

Divide both sides of $3y=-9$ by 3: $y=\frac{-9}{3}=-3$

Step3: Substitute y into one equation to find x

Substitute $y = -3$ into the first equation $x + 4y=-3$:
$x+4\times(-3)=-3$
Simplify: $x-12=-3$
Add 12 to both sides: $x=-3 + 12 = 9$

Answer:

First ordered pair: $(-1, -1)$
Second ordered pair: $(9, -3)$