Question

What is the solution of the system? Use elimination. 7x + 5y = 19 −7x − 2y = −16

Answer 1

By solving this system of equations, we find that the solution is x = 2 and y = 3.

Step-by-step explanation:

To solve this system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the two equations.

To do this, we can start by multiplying the second equation by 5 to make the coefficients of x in both equations equal. This will allow us to add the two equations and eliminate x.

Multiplying the second equation by 5, we get: -35x - 10y = -80.

Now, we can add this equation to the first equation: 7x + 5y + (-35x - 10y) = 19 + (-80).

This simplifies to: -28x - 5y = -61.

Now, we have a new equation: -28x - 5y = -61.

We can solve this equation simultaneously with the first equation to find the values of x and y.

By solving this system of equations, we find that the solution is x = 2 and y = 3.

Answer 2

Make the coefficient of y the same in both equations:

To do this, multiply equation one by 2, and equation two by 5 (this will make the coefficient 10 in both).

14x + 10y = 38
-35x - 10y = -80

Eliminate the y variable by adding the equations from each other

(14x + 10y = 38)
+ (-35x - 10y = -80)
= -21x + 0y = -42

We now have -21x = -42. The y variable has been eliminated.

Solve for x

-21x = -42

Divide both sides by -21 to get x on its own.

x = 2

Substitute x into the equation to find y.

7*2+5y=19

14+5y=19

Subtract 14 from both sides.

5y=19-14

5y=5

Divide by 5 on both sides to get y on its own.

y=5/5

y=1

The answer is (2,1)