Answer:
• Let's first assign identifications to the equations given:
• There are various methods to solve this system of equation, namely;
- <em>Graphical</em><em> </em><em>method</em>
- <em>Substitution</em><em> </em><em>method</em>
- <em>Elimination</em><em> </em><em>method</em>
- <em>Calculus</em><em> </em><em>(</em><em>Calculator</em><em> </em><em>synthetic</em><em> </em><em>method</em><em>)</em>
<u>1</u><u>.</u><u> </u><u>Graphical</u><u> </u><u>method</u><u> </u>
<u>→</u> You'll have to draw a graph, demacate it very well following the suitable scale.
→ Get values to plot from both equation (a) and equation (b).
→ Draw respective lines of each equation. The point of intersection of the lines is the answer of the values of x and y.
→ It'll be in coordinate format i.e; (x, y)
<u>2</u><u>.</u><u> </u><u>Substitution</u><u> </u><u>method</u>
→ Lemme first consider equation (a)
• make x the subject of the equation (a):
→ Considering equation (b) next
• substitute x in equation (b) with x in <u>equation</u><u> </u><u>(</u><u>c</u><u>)</u>
• then find x using equation (c)
<u>3</u><u>.</u><u> </u><u>Elimination</u><u> </u><u>method</u><u>:</u>
→ Here, we have to align the equations so that if we use addition or subtraction operations we remain with one term giving us zero [ eliminated ]
→ Multiply equation (a) by 6 and multiply equation (b) by 8. In order to eliminate x
→ Then we subtract equation (a) with equation (b)
• find x using equation (c)
<u>4</u><u>.</u><u> </u><u>Calculator</u><u> </u><u>synthetic</u><u> </u><u>method</u><u>:</u>
→ To use this method, you must have a scientific calculator.
→ If you have it, follow the steps below;
- Go to mode (<em>press</em><em> </em><em>it</em><em> </em><em>3</em><em> </em><em>times</em><em> </em><em>until</em><em> </em><em>you</em><em> </em><em>see</em><em> </em><em>"</em><em>EQN</em><em>"</em><em> </em>)
- Press 1 or any number below the "EQN". It'll display "Unknowns" with 2 and 3 below it. 2 → Two equations system. 3 → 3 equations system.
- According to our question, it is a two equations system, press 2
- It'll display a, b and c [ a is the coefficient of x, b is the coefficient of y, c is the constant]
- For a1 press 8 then press "equal sign", b1 press 9, then equal sign, c1 press -3 then equal sign.
- Follow the same procedure for a2, b2 and c2
- Automatically, It will display the answers
<u>Answer</u><u>:</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>-</u><u>1</u><u>5</u><u>,</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>1</u><u>3</u><u> </u>