Studdy AI Logo
Math  /  Algebra

Question 5) x+6y=−62x+7y=−12\begin{array}{l}\text { 5) } x+6 y=-6 \\ 2 x+7 y=-12\end{array}

Studdy Solution

STEP 1

1. We are solving a system of linear equations with two variables, x x and y y .
2. The system of equations is: $ \begin{align*} 1) & \quad x + 6y = -6 \\ 2) & \quad 2x + 7y = -12 \end{align*} \]
3. We will use the method of substitution or elimination to find the values of \( x \) and \( y \).

STEP 2

1. Choose a method to solve the system of equations.
2. Solve for one variable in terms of the other.
3. Substitute the expression into the other equation.
4. Solve for the remaining variable.
5. Substitute back to find the other variable.
6. Verify the solution by substituting both values back into the original equations.

STEP 3

We will use the elimination method to solve this system of equations.

STEP 4

To eliminate one of the variables, we will first multiply the first equation by 2 to align the coefficients of x x :
2(x+6y)=2(−6)2(x + 6y) = 2(-6)
This gives us:
2x+12y=−122x + 12y = -12

STEP 5

Now, we have the system:
\begin{align*} 1) & \quad 2x + 12y = -12 \\ 2) & \quad 2x + 7y = -12 \end{align*}
Subtract the second equation from the first to eliminate x x :
(2x+12y)−(2x+7y)=−12−(−12)(2x + 12y) - (2x + 7y) = -12 - (-12)

STEP 6

Simplify the equation:
5y=05y = 0

STEP 7

Solve for y y :
y=0y = 0

STEP 8

Substitute y=0 y = 0 back into the first equation to solve for x x :
x+6(0)=−6x + 6(0) = -6
Simplify:
x=−6x = -6

STEP 9

Verify the solution by substituting x=−6 x = -6 and y=0 y = 0 into the original equations:
For the first equation:
x+6y=−6⇒−6+6(0)=−6Truex + 6y = -6 \quad \Rightarrow \quad -6 + 6(0) = -6 \quad \text{True}
For the second equation:
2x+7y=−12⇒2(−6)+7(0)=−12True2x + 7y = -12 \quad \Rightarrow \quad 2(-6) + 7(0) = -12 \quad \text{True}
Both equations are satisfied.
The solution to the system of equations is:
(x,y)=(−6,0) \boxed{(x, y) = (-6, 0)}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord