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Solve the following system of linear equations: 2x + y = 4, 3x + 4y = 7

Mathematics

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Answer

x=95,y=25x=\frac{9}{5}, y=\frac{2}{5}

Step-by-step solution

4 steps

Given the system of equations:

{2x+y=4(1)3x+4y=7(2)\begin{cases} 2x + y = 4 \quad &(1) \\ 3x + 4y = 7 \quad &(2) \end{cases}

  1. Multiply equation (1) by 4 to make the coefficients of yy equal.

    4(2x+y)=4(4)4(2x + y) = 4(4) 8x + 4y = 16 \quad &(3)

  2. Subtract equation (2) from equation (3) to eliminate yy.

    (8x+4y)−(3x+4y)=16−7(8x + 4y) - (3x + 4y) = 16 - 7 8x+4y−3x−4y=98x + 4y - 3x - 4y = 9 5x=95x = 9

  3. Solve for xx.

    x=95x = \frac{9}{5}

  4. Substitute the value of xx into equation (1) to find yy.

    2(95)+y=42\left(\frac{9}{5}\right) + y = 4 185+y=4\frac{18}{5} + y = 4 y=4−185y = 4 - \frac{18}{5} y=205−185y = \frac{20}{5} - \frac{18}{5} y=25y = \frac{2}{5}

    The solution is x=95,y=25x=\frac{9}{5}, y=\frac{2}{5}.

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