Question

5x - 2y = -62

-9x - 5y = 60
Solve by substitution

Answer 1

from the first, you have y = (5x+62)/2

Now use that in the second equation to get
-9x - 5(5x+62)/2 = 60
x = -10
Now use that to find y

Answer 2

[AI-generated answer — Explain Bot]

To solve this system of equations by substitution, follow these steps:

Step 1: Solve one of the equations for one variable.
Let's solve the first equation, 5x - 2y = -62, for x.
Rearrange the equation to isolate x:
5x - 2y = -62
5x = 2y - 62
x = (2y - 62)/5

Step 2: Substitute the expression for x into the other equation.
Now, substitute the expression for x, which is (2y - 62)/5, into the second equation, -9x - 5y = 60.
-9((2y - 62)/5) - 5y = 60

Step 3: Solve the resulting equation for y.
Simplify the equation:
(-18y + 558)/5 - 5y = 60
Multiply both sides of the equation by 5 to eliminate the fraction:
-18y + 558 - 25y = 300
Combine like terms:
-43y + 558 = 300
Subtract 558 from both sides of the equation:
-43y = 300 - 558
-43y = -258
Divide both sides of the equation by -43:
y = -258/-43
y = 6

Step 4: Substitute the value of y back into either of the original equations to solve for x.
Let's substitute y = 6 into the first equation, 5x - 2y = -62:
5x - 2(6) = -62
5x - 12 = -62
Add 12 to both sides of the equation:
5x = -62 + 12
5x = -50
Divide both sides of the equation by 5:
x = -50/5
x = -10

Step 5: Check your solution.
Substitute the values of x = -10 and y = 6 into the second equation, -9x - 5y = 60, to verify that the solution is correct:
-9(-10) - 5(6) = 60
90 - 30 = 60
60 = 60

Therefore, the solution to the system of equations is x = -10 and y = 6.