Question

3. Consider the following system of equations.Line 1: 2x - y = -3Line 2: -6x - 2y = -6Part A:Is (0,3) a solution to Line 1? Explain your answer.Part B:Is coordinate (0, -3) is a solution to Line 2? Explain your answer.Part C:What are the slopes of Linel and Line 2?Part D:What are the y-intercepts of Line 1 and Line 2?

Answer 1

`\begin{gathered} 2x-y=-3 \\ -6x-2y=-6 \end{gathered}`

Part A

replace (0,3) on (x,y)

`\begin{gathered} 2(0)-(3)=-3 \\ 0-3=-3 \\ -3=-3 \end{gathered}`

the equivalence is correct so (0,3) is a solution of the first equation

Part B.

replace (0,-3) on (x,y)

`\begin{gathered} -6(0)-2(-3)=-6 \\ 0-(-6)=-6 \\ 6=-6 \end{gathered}`

the equivalence is incorrect so (0,-3) isnt a solution of the second equation

Part C

To find the slope we need to solve each expresion and take the coefficient of x

first equation

`\begin{gathered} 2x-y=-3 \\ y=2x+3 \end{gathered}`

the slope is 2

second equation

`\begin{gathered} -6x-2y=-6 \\ 2y=-6x+6 \\ y=-3x+3 \end{gathered}`

the slope is -3

Part D

the y-intercept is the constant without variable on each equation

first equation

`y=2x+3`

the y-intercept is 3

second equation

`y=-3x+3`

the y-intercep is 3 too

The Graph

we need two points of the line and join by a right infinite line

first equation

the points (0,3) and (-3/2,0) belong to the line 1

second equation

the points (0,3) and (1,0) belong to the line 2

Solution of the system

we can note the two lines trought the point (3,0) so this is the solution and we can check matching the equations and solving x

`\begin{gathered} 2x+3=-3x+3 \\ 2x+3x=3-3 \\ 5x=0 \\ x=0 \end{gathered}`

and replace x=0 on any equation to solve y I will use the first equation

`\begin{gathered} y=2x+3 \\ y=2(0)+3 \\ y=3 \end{gathered}`

so the solution point is (0,3)