Given the simultaneous equations

2x + 3y = 0.75 (1)

5x + 2y = 6 (2)

Solve for x and y algebraically.

Step-by-Step

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In these two equations, neither the x- nor the y-terms are the same. If equation (1) is multiplied by 2 and equation (2) is multiplied by –3, the y-terms in both equations will be the same with opposite signs. Then proceed as in Worked Example 3.1 above.

**Step 1:** Eliminate y-terms from the system of equations:

4x + 6y = 1.5 (1)× 2

\underline {−15x − 6y = 18} (2)×−3

−11x = −16.5 adding

x = \frac {−16.5}{−11}= 1.5 solving for x

**Step 2:** Solve for y by substituting x = 1.5 into either equation (1) or equation (2):

2(1.5) + 3y = 0.75 substituting x = 1.5 into equation (1)

3y = 0.75 − 3

y = \frac {−2.25}{3}

**Step 3:** Checking the solution: x = 1.5, y = −\frac {2.25}{3} is left as an exercise for the reader.

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