Question

Solve the system of equations:

{ −3y+5x=26
−2y−5x=−16}
A) x=3,y=5
B) x=−2,y=−4
C) x=2,y=−6​
D) x=−3,y=7

Answer 1

The solution to the system of equations {-3y + 5x = 26, -2y - 5x = -16} is found by adding the two equations to eliminate x, which gives y = -2. Substituting y = -2 into one of the original equations and solving for x gives x = 4.

Step-by-step explanation:

To solve the system of equations:

• −3y + 5x = 26
• −2y − 5x = −16

We can add the two equations to eliminate the variable x:

(-3y + 5x) + (-2y - 5x) = 26 - 16

This simplifies to:

-5y = 10

Divide both sides by -5 to solve for y:

y = -2

Now we can substitute y = -2 into one of the original equations to find x. Let's use the first equation:

-3(-2) + 5x = 26

6 + 5x = 26

Subtract 6 from both sides:

5x = 20

Divide by 5:

x = 4

Therefore, the solution to the system of equations is x = 4 and y = -2.