Question

What is the solution of the system?
7x + 5y = 19
-7x-2y=-16
(1 point)
(2, 1)
(1, 2)
(7,5)
(-7,-2)

Answer 1

To solve the system of equations, we can use the method of elimination or substitution. Let's use the method of elimination.

First, let's multiply the second equation by -1 to eliminate the x-term:
-(-7x-2y) = -(–16)
7x + 2y = 16

Now we can add the two equations together:
(7x + 5y) + (7x + 2y) = 19 + 16
14x + 7y = 35

Next, let's divide this equation by 7 to simplify:
(14x + 7y)/7 = 35/7
2x + y = 5

Now we have a new system of equations:
2x + y = 5
7x + 5y = 19

We can solve this system by substitution or elimination. Let's use elimination again.

Multiply the first equation by 5 and the second equation by -1 to eliminate the y-term:
5(2x + y) = 5(5)
-1(7x + 5y) = -1(19)

10x + 5y = 25
-7x - 5y = -19

Now add the two equations together:
(10x + 5y) + (-7x - 5y) = 25 - 19
3x = 6

Divide both sides of the equation by 3:
3x/3 = 6/3
x = 2

Now substitute this value of x into one of the equations to solve for y. Let's use the first equation:
2(2) + y = 5
4 + y = 5

Subtract 4 from both sides of the equation:
4 + y - 4 = 5 - 4
y = 1

Therefore, the solution to the system of equations is (x, y) = (2, 1).