Question

Consider the system of linear equations.

Answer 1

2y = x + 10
3y = 3x + 15
multiply the first by 3
6y=3x+10
6y-10=3x
put 6y-10 in place of 3x in the second one
3y=6y-10+15
-3y=5
y=-5/3
x=-20/3
these statements are true based on answer
The system has one solution.
Both lines have the same y-intercept.
The solution is the intersection of the 2 lines

Answer 2

Answer:

Statement 1 : True

Statement 2: False

Statement 3: False

Statement 4:True

Statement 5:False

Statement 6:True

Step-by-step explanation:

Given : $2y = x + 10$

           $3y = 3x + 15$

To Find: Which statements about the system are true?

Solution:

Slope intercept form: $y =mx+c$

where m is the slope

Convert the given equations in slope intercept form

Equation 1: $2y = x + 10$

$y = \frac{x}{2}+\frac{10}{2}$

$y = \frac{x}{2} +5$  --A

On comparing with general form

Slope = m = $\frac{1}{2}$

Equation 2: $3y = 3x + 15$

$y = \frac{3}{3}x + \frac{15}{3}$

$y = x +5$  --B

On comparing with general form

Slope = m = 1

Substitute the value of x form B in A

$y = \frac{y-5}{2} +5$

$y-5 = \frac{y-5}{2}$

$2y-10 = y-5$

$y=5$

Substitute the value of y in B to get value of x

$5 = x +5$

$x=0$

Thus the solution is (0,5)

Thus The system has one solution.

So, Statement 1 is true

Since the slopes of the given lines are not same so the lines are not parallel

Thus the statement 2 is false.

Slope of line 1 is $\frac{1}{2}$ and slope of line 2 is 1

Since the slopes are not same

So, statement 3 is false.

Equation 1: $2y = x + 10$

To find y intercept substitute x =0

$2y = 0 + 10$

$y =\frac{10}{2}$

$y =5$

Equation 2: $3y = 3x + 15$

To find y intercept substitute x =0

$3y = 3(0) + 15$

$y =\frac{15}{3}$

$y =5$

So,statement 4 is true Both lines have the same y-intercept.

Statement 5: The equations graph the same line.

Statement 5 is false (refer the attached graph)

Statement 6 is true The solution is the intersection of the 2 lines (refer the attached graph)