The document Solved Equations - Linear Equations GMAT Notes | EduRev is a part of the GMAT Course Quantitative Aptitude for GMAT.

All you need of GMAT at this link: GMAT

Section - 1**Ques 1: If x = 2, then x ^{2} - 4x + 3 =Ans: **x

(2)

4 - 8 + 3 = -1

Ans:

Ans:

Ans:

Ans:

Now, to find the value of y, we need to isolate y on one side of the equation.

Solve for the variable in the following equations.

-3x = -12

x= 4

Subtract 14

Divide by -3

Ans:

21 - 3x = 6

- 3x = -15

x= 5

Simplify

Subtract 21

Divide by -3

Ans:

5x+ 13 = -7

5x= -20

x = -4

Subtract 2x

Subtract 13

Divide by 5

Ans:

3t

t

t= 3

Ans:

Ans:

1,200x= 7,200

x = 6

Ans:

Isolate x in the following equations.

Ques 13:

3x + 2x + 4 = 2x + 16

5x + 4 = 2x + 16

3x + 4 = 16

3x = 12

x = 4

Ans:

3x + 7 = 10x

7 = 7x

1 = x

Ans:

-12 x - 32 = - 8x + 72

-32 = 4 x+ 72

-104 = 4x

-26 = x

Ans:

-x + 15 = -4x - 12

3x + 15 = -12

3x = -27

x = -9

Ans:

2x(-2) = -2x + 12

-4x= -2x + 12

- 2x = 12

x = -6

**Solve for the values of both variables in each system of equations using substitution. The explanations will use substitution to solve.Ques 18: 7x - 3y = 5y= 10Ans:** 7x - 3y = 5,y= 10

7x - 3(10) = 5

7x - 30 = 5

7x = 35

x = 5

Answer: x= 5 ,y= 10

y = 7 x - 5

Ans:

10 = 3x - 5

15 = 3x

5 = x

7 = 4(5) + 10

y - 30

Answer:x = 5, y = 30

Ans:

2h - 4h +12 =0

-2h = - 12

h = 6

k= (6) - 3

k = 3

Answer: h = 6, k = 3

Solve for the values of both variables in each system of equations using elimination. The explanations will use elimination to solve.

Ques 21: x -y = 4

Ans:

Therefore x = 3 and plugging this back in to the first equation yields:

Answer: x - 3 and 7 = â€”1

x-4y = -7

Ans:

The new equation simplifies to 67 = 12, or7 = 2. Then, we plug this value for7 into the first equation to get x + 2(2) = 5, or x = 1.

Notice that we must be very careful to change the sign of each term in the second equation when subtracting. Alternatively, we could have multiplied the entire second equation by -1 to get -x+4 y = 7 and then added this equation to the first:

This yields the same solution: y = 2 and x = 1.

Ans:

Hence a = 5. Then, we plug this value for a into the first equation to get (5) + b = 8, or b = 3.

Answer: a = 5, b = 3

Ques 24:

Therefore x = 1. We can now plug this value for x in to either of the original equations to solve for y, but it will be easiest to plug in to the equation that was used for the substitution (after all, it is already solved for y). Hence y = (1/2) x (1) + 3 = 3.5.

Answer: x = 1, y = 3.5

2y = x + 1

If we use substitution, it is best to solve the first equation for y, giving us y = x + 3, and then substitute this into the second equation:

We then plug this into the equation used for the substitution step to get y = (-5) + 3 = -2.

Answer: x = -5 , y = -2

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

85 videos|100 docs|176 tests

### Test: Problems On Ages - 1

- Test | 10 ques | 20 min
### Test: Problems On Ages - 2

- Test | 20 ques | 40 min

- How to Solve Number of Integral Solutions
- Doc | 8 pages
- Test: Linear Equations- 2
- Test | 15 ques | 15 min
- Test: Linear Equations- 1
- Test | 10 ques | 20 min