Studdy AI Logo
Math  /  Algebra

QuestionUSE SUBSTITUTION TO SOLVE EACH LINEAR SYSTEM - To get full marks, you need to check and show 3x−y=−74x+2y=−6\begin{array}{l} 3 x-y=-7 \\ 4 x+2 y=-6 \end{array}

Studdy Solution

STEP 1

1. We are given a system of two linear equations.
2. We will use the substitution method to solve the system.
3. The solution involves finding the values of x x and y y that satisfy both equations.
4. We will check the solution by substituting the values back into the original equations.

STEP 2

1. Solve one of the equations for one variable.
2. Substitute the expression from Step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute back to find the value of the first variable.
5. Check the solution by substituting both values into the original equations.

STEP 3

Choose the first equation to solve for y y :
3x−y=−7 3x - y = -7
Rearrange to express y y in terms of x x :
y=3x+7 y = 3x + 7

STEP 4

Substitute the expression for y y from Step 1 into the second equation:
4x+2(3x+7)=−6 4x + 2(3x + 7) = -6

STEP 5

Simplify the equation:
4x+6x+14=−6 4x + 6x + 14 = -6
Combine like terms:
10x+14=−6 10x + 14 = -6

STEP 6

Solve for x x :
10x=−6−14 10x = -6 - 14
10x=−20 10x = -20
x=−2 x = -2

STEP 7

Substitute x=−2 x = -2 back into the expression for y y :
y=3(−2)+7 y = 3(-2) + 7
y=−6+7 y = -6 + 7
y=1 y = 1

STEP 8

Check the solution by substituting x=−2 x = -2 and y=1 y = 1 back into the original equations:
First equation: 3x−y=−7 3x - y = -7
3(−2)−1=−7 3(-2) - 1 = -7
−6−1=−7 -6 - 1 = -7
True.
Second equation: 4x+2y=−6 4x + 2y = -6
4(−2)+2(1)=−6 4(-2) + 2(1) = -6
−8+2=−6 -8 + 2 = -6
True.
Both equations are satisfied.
The solution to the system is:
x=−2, y=1 x = -2, \, y = 1

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