How do you solve the system of equations 3x+y=23 and 4xy=19?

2 Answers
Jan 7, 2018

X=6, Y=5

Explanation:

Use simultaneous equations (multiplying both equations, and eliminating either x or y by adding or subtracting to find the value of one, then plugging the value back in to find the other value)

The lowest common multiple of 3 and 4 is 12
34=12 so we have to multiply the first equation by 4
43=12 so we have to multiply the second equation by 3

This is the result:
12x+4y=92
12x3y=57

From here as x is the same, you can subtract the bottom equation from the top leaving you with y. After doing this the result is:

7y=35
y=357=5

Then we can plug this value back into the equations, then we can solve to find x.
3x+y=23
3x+5=23
3x=18 (-5)
x=183=6

We have got x=6 and y=5, but we have to check if these values work for both equations so lets check.

4xy=19
465=19
245=19

So therefore these values fit both equations and we are correct.

Jan 7, 2018

The point of intersection is (6,5)

Explanation:

You can also use substitution. The resulting values for x and y are the point of intersection of the two equations.

Equation 1: 3x+y=23

Equation 2: 4xy=19

Solve Equation 1 for y.

3x+y=23

Subtract 3x from both sides.

y=233x

Substitute 233x for y in Equation 2 and solve for x.

4xy=19

4x(233x)=19

Simplify.

4x23+3x=19

Add 23 to both sides.

4x+3x=19+23

Simplify.

7x=42

Divide both sides by 7.

x=427

x=6

Substitute 6 for x into Equation 1 and solve for y.

3x+y=23

3(6)+y=23

Simplify.

18+y=23

Subtract 18 from both sides.

y=2318

y=5

The point of intersection is (6,5).

Equation 1:

3(6)+5=23

18+5=23

23=23

Equation 2:

4(6)5=19

245=19

19=19

graph{(y+3x-23)(-y+4x-19)=0 [-15.69, 16.34, -5.83, 10.19]}