Question

Solve the system of linear equations by adding or subtracting.

3x + 7y = −17
4x − 7y = 10


Enter your answer as an ordered pair.

Answer 1

To solve the provided system of linear equations, add the two equations to eliminate the y-terms and solve for x. Then substitute the value of x into one of the original equations to find y. The solution is the ordered pair (-1, -2).

Step-by-step explanation:

To solve the system of linear equations by adding or subtracting, we should look at the given equations:

3x + 7y = −17

4x − 7y = 10

We notice that the coefficients of y in both equations have the same magnitude but opposite signs, which makes them ideal for elimination by addition. Let's add the two equations together:

(3x + 7y) + (4x − 7y) = −17 + 10
7x = −7
x = −7 / 7
x = −1

Now that we have the value of x, we substitute it into one of the original equations to find y:

3(−1) + 7y = −17
−3 + 7y = −17
7y = −17 + 3
7y = −14
y = −14 / 7
y = −2

The solution to the system of equations is the ordered pair (−1, −2).

Answer 2

3x + 7y = −17

4x − 7y = 10

Add up both sides of 2 equations, then

7x = -7

=> x = 1

=> y =(3 x 1 - 17)/7 = -14/7 = -2

Hope this helps!

:)