Question

Can someone help me with system of equations?

y = 5x + 7

y = 2x + 10

and

y = 2x + 18

9y = -2x+2

Please let me know if substitution or elimination is used.

Answer 1

for the first set of equations, it’s easier to use substitution because both equations are already equal to y.

5x + 7 = 2x + 10

- 7 - 7

5x = 2x + 3

- 2x = - 2x

3x = 3

/3 /3

x = 1

now that you solved for x, plug 1 into an equation to find y

y = 5(1) + 7

y = 5 + 7

y = 12

so the answer is (1,12)

for the next one, use elimination because there is a positive/negative +-2x pair

y = 2x + 18

9y = -2x + 2

the 2x and the -2x will cancel out. add the other terms

10y = 20

divide both sides by 10

y = 10

now that we have the y term, plug it in to solve for x

10 = 2x + 18

-18 -18

-8 = 2x

-4 = x

the answer is (-4,10)

Answer 2

#1)

Answer:

x=1 and y=12

Step-by-step explanation:

y=5x+7

y=2x+10

This system should use substitution because the value of y is given in terms if x.

Substitution:

5x+7=2x+10

Solve:

3x=3

x=1

Substitute x to solve for y by plugging x into one if the original equations(doesn’t matter which one is used).

y=5x+7

y=5(1)+7

y=5+7

y=12

#2)

Answer:

x=-8 and y=2

Step-by-step explanation:

y=2x+18

9y=-2x+2

This system also uses substitution. The value of y us already given in terms if c in the first equations, so we will substitute in the second equation.

Substitute:

9(2x+18)=-2x+2

Solve:

18x+162=-2x+2

20x=-160

x=-8

Now that we have the value if x, plug it into one of the original equations(doesn’t matter which equation) and substitute to find y.

y=2x+18

Substitute:

y=2(-8)+18

Solve:

y=-16+18

y=2