Is (2,10) a soulution of y = 4x + 2 & y = x + 2?

Question

I need the help because in 2 weeks I am going to take a test about systems of equations.

Answer 1

(2,10) a soulution of y = 4x + 2 & y = x + 2?I need the help because in 2 weeks I am going to take a test about systems of equations.

 

Solution:

 

all you have to do is substitute the values of the point (2,10) in the equations x=2, y=10, both equations must be satisfied

 

The equation are y = 4x + 2 ...eq1 & y = x + 2 ...eq2

from the 1st equation 10=4(2)+2, 10=10 1st equation is satisfied

from the 2nd equation 10≠2+2 = 4 2nd equation is not satisfied

 

Therefore the point (2,10) is not a solution to the system of equations

the solution be found by the solving the two equations two unknowns system

y=4x+2 ...Eq1

y=x+2 ...Eq2 Multiply by -1

 

y=4x+2 ...Eq1
-y=-x-2 ...Eq2 Add equations

 

0=4x-x+2-2, 0=3x, x=0 , from eq ..2 y=0+2 =2 the point (0,2) is a solution Check:

 

y=4x+2 ...Eq1, 2=4(0)+2, 2=2 satisfied

y=x+2  ...Eq2, 2=0+2, 2=2 satisfied the point (0,2) satisfies both equations and is a solution

 

Answer 2

To check is (2, 10) is a solution of 

y = 4x + 2

y = x + 2

or not, you have to plug in x=2 and y=10 into the system of equations:

10=4*2+2 --> 10=10 good

10 =2+2  --->10=4 not

So, (2, 10) is not a solution.