Studdy AI Logo
Math  /  Algebra

Questionain an equation in one variable to solve the system by substitution.
2. y=−8x+2y=-8 x+2 2x+y=−102 x+y=-10

Studdy Solution

STEP 1

1. We are given a system of two linear equations in two variables.
2. The goal is to find the values of x x and y y that satisfy both equations.
3. We will use the substitution method to solve the system.

STEP 2

1. Identify the equation that is already solved for one variable.
2. Substitute the expression for the solved variable into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute back to find the other variable.
5. Check the solution by substituting both values into the original equations.

STEP 3

The first equation is already solved for y y :
y=−8x+2 y = -8x + 2

STEP 4

Substitute the expression for y y from the first equation into the second equation:
2x+(−8x+2)=−10 2x + (-8x + 2) = -10

STEP 5

Simplify and solve the equation for x x :
Combine like terms:
2x−8x+2=−10 2x - 8x + 2 = -10
−6x+2=−10 -6x + 2 = -10
Subtract 2 from both sides:
−6x=−12 -6x = -12
Divide both sides by −6-6:
x=2 x = 2

STEP 6

Substitute x=2 x = 2 back into the expression for y y :
y=−8(2)+2 y = -8(2) + 2
Simplify:
y=−16+2 y = -16 + 2
y=−14 y = -14

STEP 7

Check the solution by substituting x=2 x = 2 and y=−14 y = -14 into the original equations:
First equation:
y=−8x+2 y = -8x + 2
−14=−8(2)+2 -14 = -8(2) + 2
−14=−16+2 -14 = -16 + 2
−14=−14 -14 = -14 (True)
Second equation:
2x+y=−10 2x + y = -10
2(2)+(−14)=−10 2(2) + (-14) = -10
4−14=−10 4 - 14 = -10
−10=−10 -10 = -10 (True)
Both equations are satisfied.
The solution is:
x=2, y=−14 x = 2, \, y = -14

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord