Question

Solve this system of equations using any method.

2x – y = 5
4x + y = 7


(2, –4)


(4, –9)


(2, –1)


(4, –3)

Answer 1

(2, –1)

Explanation:

Substitution Method

2x – y = 5 and 4x + y = 7 are two given equation

Step 1:

Name the Equation

2x – y = 5 ...(1)

4x + y = 7 ...(2)

Step 2:

From equation (1) we get,

2x = y + 5

x = y + 5/2

Step 3:

Substitute the value of x in equation (2)

i.e.,

4(y + 5/2) + y = 7

2(y + 5) + y = 7

2y + 10 + y = 7

3y = 7 - 10

3y = -3

y = -3/3

y = -1

Step 4:

Now, Substitute the value of y in equation (1)

i.e.,

2x – (-1) = 5

2x + 1 = 5

2x = 5 - 4

2x = 4

x = 4/2

x = 2

VERIFICATION:

2(2) – (-1) = 5 i.e., 4 + 1 = 5

4(2) + (-1) = 7 i.e., 8 - 1 = 7