Question

Solve the system of linear equations. 2x + 5y = 12 4x − y = 2

Answer 1

x = 1, y = 2 → (1, 2)

Explanation:

`\left\{\begin{array}{ccc}2x+5y=12\\4x-y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+5y=12\\20x-5y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad22x=22\qquad\text{divide both sides by 22}\\.\qquad x=1\\\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\4(1)-y=2\\4-y=2\qquad\text{subtract 4 from both sides}\\-y=-2\qquad\text{change the signs}\\y=2`

Answer 2

x=1, y=2. (1, 2).

Explanation:

2x+5y=12

4x-y=2

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y=4x-2

2x+5(4x-2)=12

2x+20x-10=12

22x-10=12

22x=12+10

22x=22

x=22/22

x=1

4(1)-y=2

4-y=2

y=4-2=2

y=2