Question

In: Advanced Math

For the following exercises, determine whether the given ordered pair is a solution to the system of equations. x + 8y = 43 3x − 2y = −1 and (3, 5)

For the following exercises, determine whether the given ordered pair is a solution to the system of equations.

x + 8y = 43

3x − 2y = −1 and (3, 5)

Solutions

Expert Solution

Consider the system of linear equations in two variables as

a1x + b1y = c1

a2x + b2y = c2

 

The solution of such system of linear equations in two variables is any ordered pair that satisfies each equation independently.

 

Consider system of equations as:

x + 8y = 43 …… (1)

3x – 2y = -1 …… (2)

 

Verify if ordered pair (3, 5) is solution of (1) and (2).

 

Substitute x = 3 and y = 5 in (1) and proceed as following:

(3) + 8(5) = 43

    3 + 40 = 43

          43 = 43

 

Thus, (3, 5) satisfies (1).

 

Now, substitute x = 3 and y = 5 in (2) as shown below:

3(3) – 2(5) = -1

       9 – 10 = -1

              -1 = -1

 

Thus, (3, 5) satisfies (2).

 

Therefore, given ordered pair (3, 5) is a solution of given system of linear equations.


Therefore, given ordered pair (3, 5) is a solution of given system of linear equations.

Related Solutions

For the following exercises, determine whether the given ordered pair is a solution to the system of equations. −2x + 5y = 7 2x + 9y = 7 and (−1, 1)
For the following exercises, determine whether the given ordered pair is a solution to the system of equations.−2x + 5y = 72x + 9y = 7 and (−1, 1)
Solve the simultaneous equations: a) x + y = 7, 3x - 2y = 11 b) 7x - 2y = 1, 3x + 4y = 15?
Solve the simultaneous equations:a) x + y = 7,  3x - 2y = 11b) 7x - 2y = 1, 3x + 4y = 15
2. Given the System of Equations: 3x+2y+z+20w= 6 x+2y+z+10w=0 x+y+z+6w=2 2x+2y+z+15w=3 a) Use your calculator to...
2. Given the System of Equations: 3x+2y+z+20w= 6 x+2y+z+10w=0 x+y+z+6w=2 2x+2y+z+15w=3 a) Use your calculator to solve, leaving solution in parametric form b) Find the specific solution when y = 6 c) Perform, BY HAND, a full check of this particular solution
For the following exercises, determine whether or not the given function f is continuous everywhere....f(x) = 2x + 5/x
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = 2x + 5/x
Question 1 Using MATLAB solve the following system of linear simultaneous equations 3x + 2y -...
Question 1 Using MATLAB solve the following system of linear simultaneous equations 3x + 2y - z = 10........... [1] -x + 3y + 2z = 5........... [2] x - y - z = -1 .................[3] s + 2t - 3u + 4v = 12........... [1] 2s + 2t - 2u + 3v = 10......... [2] t + u = -1............................ [3] s - t + u - 2v = -4................ [4]
For the following exercises, determine whether or not the given function f is continuous everywhere....f(x) = sec(x) − 3.
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = sec(x) − 3.
Solve the system of equations: x+y^2=6y x-2y=-5
Solve the system of equations: x+y^2=6y x-2y=-5
For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = log2 (x)
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = log2 (x)
For the following exercises, determine whether or not the given function f is continuous everywhere...f(x) = tan(x) + 2
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = tan(x) + 2
Solve for x,y,z if there if a solution to the given system of linear equations: x...
Solve for x,y,z if there if a solution to the given system of linear equations: x - 3y - 2z = -3 3x + 2y - z = 12 -x - y + 4z = 3
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT