MATH SOLVE

3 months ago

Q:
# Need help asap!! will rate 5 stars!!A system of equations is shown below:n = 3m + 7n − 2m = 1What is the solution, in the form (m, n), to the system of equations? (3, 7) (1, 8) (−3, −2) (−6, −11)Which statement is true about the solutions for the equation 4y + 6 = −2? It has infinitely many solutions. It has two solutions. It has one solution. It has no solution.The system of equations shown below is graphed on a coordinate grid:3y + x = 42y − x = 6Which statement is true about the coordinates of the point that is the solution to the system of equations? It is (−2, 2) and lies on both lines. It is (−5, 3) and lies on both lines. It is (−5, 3) and does not lie on either line. It is (−2, 2) and does not lie on either line.What is the value of z in the equation 2z + 6 = −4? 5 1 −1 −5Which statement is true for the equation 2x − 2x − 7 = −7? It has infinitely many solutions. It has two solutions. It has one solution. It has no solution.The incomplete work of a student to solve an equation is shown below:Step 1: 4x + 12 = 4Step 2: ?Step 3: x = −8 ÷ 4Step 4: x = −2What is the missing Step 2? 4x = 8 4x = 16 4x = −16 4x = −8Which set of steps shows the solution to the equation 2y = −8? y = −8 − 2; y = 6 y = −8 ÷ (−2); y = 4 y = −8 ÷ 2; y = −4 y = −8 − (−2); y = −6A system of two equations is shown below:Equation C: a = 3b + 6Equation D: a = 7b − 1What value of a can be substituted into equation D to solve the system of equations? 3b 7b 3b + 6 7b − 1

Accepted Solution

A:

Answer:1. (-6, -11)2. It has one solution3. It is (−2, 2) and lies on both lines4. [tex]-5[/tex]5. It has infinitely many solutions.6. [tex]4x=-8[/tex]7. y = −8 ÷ 2; y = −48. 3b + 6

Step-by-step explanation:

Question 1:Substituting equation 1 into equation 2 and solving for [tex]m[/tex] gives us:[tex]n-2m=1\\(3m+7)-2m=1\\m+7=1\\m=1-7\\m=-6[/tex]Plugging this value into equation 1 gives us [tex]n[/tex], so we have:[tex]n=3m+7\\n=3(-6)+7\\n=-18+7\\n=-11[/tex]Hence, the solution, in the form (m, n), to the system of equations is (-6,-11).

Question 2:Solving the equation for [tex]y[/tex] gives us:[tex]4y+6=-2\\4y=-2-6\\4y=-8\\y=\frac{-8}{4}=-2[/tex]As we can see, there is only one solution.

Question 3:We can add the both equations so [tex]x[/tex] cancels out and then we can solve for [tex]y[/tex]:[tex](3y+x=4)\\+(2y-x=6)\\---------\\5y=10\\y=\frac{10}{5}=2[/tex]Substituting this value of [tex]y[/tex] into any equation above (let's use equation 1) will give us [tex]x[/tex]:[tex]3y+x=4\\3(2)+x=4\\6+x=4\\x=4-6\\x=-2[/tex]So the intersection point (or solution) (-2, 2) lies on both the lines.

Question 4:Let's do some algebra and figure out the value of [tex]z[/tex]:[tex]2z+6=-4\\2z=-4-6\\2z=-10\\z=\frac{-10}{2}=-5[/tex][tex]z[/tex] is -5

Question 5:Reducing the equation gives us:[tex]2x-2x-7=-7\\0-7=-7\\-7=-7[/tex]We can plug in ANY VALUE into [tex]x[/tex] and make this equation true. So there are INFINITELY MANY SOLUTIONS.

Question 6:Step 2 of the solution should be taking 12 to the other side so that variable is on one side and all the numbers to the other. So 2nd step would be:[tex]4x+12=4\\4x=4-12\\4x=-8[/tex]Rest of the steps follow. So, 2nd step would be [tex]4x=-8[/tex].

Question 7:The next step to solving this equation would be to DIVIDE -8 by 2 since 2 is multiplied with [tex]y[/tex]. [tex]2y=-8\\y=\frac{-8}{2}=-4[/tex]Third answer choice is right.

Question 8:We can substitute the value of [tex]a[/tex] given in Equation C into Equation D to solve the system of equations.The value of [tex]a[/tex] in Equation C is given as [tex]a=3b+6[/tex]Third answer choice is right.

Step-by-step explanation:

Question 1:Substituting equation 1 into equation 2 and solving for [tex]m[/tex] gives us:[tex]n-2m=1\\(3m+7)-2m=1\\m+7=1\\m=1-7\\m=-6[/tex]Plugging this value into equation 1 gives us [tex]n[/tex], so we have:[tex]n=3m+7\\n=3(-6)+7\\n=-18+7\\n=-11[/tex]Hence, the solution, in the form (m, n), to the system of equations is (-6,-11).

Question 2:Solving the equation for [tex]y[/tex] gives us:[tex]4y+6=-2\\4y=-2-6\\4y=-8\\y=\frac{-8}{4}=-2[/tex]As we can see, there is only one solution.

Question 3:We can add the both equations so [tex]x[/tex] cancels out and then we can solve for [tex]y[/tex]:[tex](3y+x=4)\\+(2y-x=6)\\---------\\5y=10\\y=\frac{10}{5}=2[/tex]Substituting this value of [tex]y[/tex] into any equation above (let's use equation 1) will give us [tex]x[/tex]:[tex]3y+x=4\\3(2)+x=4\\6+x=4\\x=4-6\\x=-2[/tex]So the intersection point (or solution) (-2, 2) lies on both the lines.

Question 4:Let's do some algebra and figure out the value of [tex]z[/tex]:[tex]2z+6=-4\\2z=-4-6\\2z=-10\\z=\frac{-10}{2}=-5[/tex][tex]z[/tex] is -5

Question 5:Reducing the equation gives us:[tex]2x-2x-7=-7\\0-7=-7\\-7=-7[/tex]We can plug in ANY VALUE into [tex]x[/tex] and make this equation true. So there are INFINITELY MANY SOLUTIONS.

Question 6:Step 2 of the solution should be taking 12 to the other side so that variable is on one side and all the numbers to the other. So 2nd step would be:[tex]4x+12=4\\4x=4-12\\4x=-8[/tex]Rest of the steps follow. So, 2nd step would be [tex]4x=-8[/tex].

Question 7:The next step to solving this equation would be to DIVIDE -8 by 2 since 2 is multiplied with [tex]y[/tex]. [tex]2y=-8\\y=\frac{-8}{2}=-4[/tex]Third answer choice is right.

Question 8:We can substitute the value of [tex]a[/tex] given in Equation C into Equation D to solve the system of equations.The value of [tex]a[/tex] in Equation C is given as [tex]a=3b+6[/tex]Third answer choice is right.