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Solve the system of linear equations by substitution. Check your solution.

Solve the system of linear equations by substitution. Check your solution.-example-1
User Shiniece
by
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1 Answer

4 votes

Answer:


x = 1.5


y =1

Explanation:

Given


4x + 2y = 8


6x - 4y = 5

Required

Solve for x and y


4x + 2y = 8 --- (1)


6x - 4y = 5 --- (2)

Divide equation (1) through by 2


(1)/(2)(4x + 2y) = 8*(1)/(2)


2x + y = 4

Make y the subject


y = 4 - 2x

Substitute 4 - 2x for y in equation (2)


6x - 4y = 5


6x - 4(4- 2x) = 5

Open bracket


6x - 16+ 8x = 5

Collect Like Terms


6x + 8x = 5+16


14x = 21

Solve for x


x = (21)/(14)


x = 1.5

Substitute 1.5 for x in
y = 4 - 2x


y = 4 - 2(1.5)


y = 4 - 3


y =1

To check the solution:

Substitute the values of x and y i the equations


4x + 2y = 8


4 * 1.5 + 2 * 1 = 8


8 = 8


6x - 4y = 5


6 * 1.5 - 4 * 1 = 5


5 = 5

Hence, the solution is true

User JosephH
by
8.4k points

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