Question21 0 ** 201-4) What is the solution to the system of equations below? 1) no solution y=2x+8 3(-2x+y)=12 2) infinite solutions 3) (-1,6) 4) 2.9 boxes of cookies to bring to a contains 12 cookies. She decides for herself. She brings 60 ty. Which equation can be used of boxes, x, Kendal bought? 6. The graph of the equation x+3y=6 intersects the y-axis at the point whose coordinates are 1) (0,2) 2) (0,6) 3) (0,18) 4) (6,0)
Studdy Solution
STEP 1
What is this asking? We need to solve a system of equations to find out if there's no solution, infinite solutions, or a specific point that satisfies both equations. Watch out! Don't forget to check if the lines are parallel or the same line, which would mean no solution or infinite solutions, respectively!
STEP 2
1. Write the equations in standard form
2. Check for parallel lines or identical lines
3. Solve the system of equations
STEP 3
Let's start by writing both equations in a standard form, which is .
The first equation is already in slope-intercept form: .
To convert it, we subtract from both sides:
\[
-2x + y = 8 $The second equation is \(3(-2x + y) = 12\).
Let's distribute the to both terms inside the parentheses:
\[
-6x + 3y = 12 $
STEP 4
Now, let's compare the coefficients of and in both equations:
First equation:
Second equation:
If we divide the entire second equation by , we get:
\[
-2x + y = 4 $
STEP 5
Notice that the coefficients of and are the same, but the constants on the right side are different ( and ).
This means the lines are parallel and do not intersect.
So, there is **no solution**!
STEP 6
Since we determined the lines are parallel, there's no need to solve further.
The system has **no solution**.
STEP 7
The solution to the system of equations is **no solution**.
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