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Solve the simultaneous equations:

[tex]\[
\begin{array}{l}
2x + 3y = 13 \\
4x - y = -2
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Let's solve the simultaneous equations step-by-step:

1. Equations Given:
[tex]\[ \begin{array}{l} 2x + 3y = 13 \quad \cdots (1) \\ 4x - y = -2 \quad \cdots (2) \end{array} \][/tex]

2. Express one variable in terms of the other using Equation (2):
[tex]\[ 4x - y = -2 \implies y = 4x + 2 \quad \cdots (3) \][/tex]

3. Substitute the expression for [tex]\( y \)[/tex] from Equation (3) into Equation (1):
[tex]\[ 2x + 3(4x + 2) = 13 \][/tex]
[tex]\[ 2x + 12x + 6 = 13 \][/tex]
[tex]\[ 14x + 6 = 13 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
[tex]\[ 14x = 13 - 6 \][/tex]
[tex]\[ 14x = 7 \][/tex]
[tex]\[ x = \frac{7}{14} \][/tex]
[tex]\[ x = \frac{1}{2} \][/tex]

5. Substitute [tex]\( x = \frac{1}{2} \)[/tex] back into Equation (3) to find [tex]\( y \)[/tex]:
[tex]\[ y = 4 \left( \frac{1}{2} \right) + 2 \][/tex]
[tex]\[ y = 2 + 2 \][/tex]
[tex]\[ y = 4 \][/tex]

6. Solution:
[tex]\[ \boxed{x = \frac{1}{2}, \, y = 4} \][/tex]

Thus, the solution to the simultaneous equations is [tex]\( x = \frac{1}{2} \)[/tex] and [tex]\( y = 4 \)[/tex].
chibabykalu16

Answer:

x = 0.5

y = 4

Step-by-step explanation:

Given:

  • 2x + 3y = 13 (Equation 1)
  • 4x - y = -2 (Equation 2)

Firstly, make y the subject of the formula in equation 2 for simplicity.
Note: you can still use Equation 1 if you want to do so.

4x - y = -2

4x - y + 2 = -2 + 2

4x + 2 - y + y = y
y = 4x + 2 (Let's call that Equation 3)

Next step, Substituting equation 3 to equation 1

What is substitution?

Substitution in simutaneous equations is the process of inserting values of variables into other equations.

For example, x = 3 and y = 2x then y = 2 * 3 = 6

2x + 3y = 13

Where:

  • y = 4x + 2

2x + 3(4x + 2) = 13

2x + 12x + 6 = 13

14x = 13 - 6

14x = 7

x = 7/14 = 1/2 = 0.5

The value of x simplifies to 0.5 or [tex]\frac{1}{2} \text{ in fraction}[/tex]

Using the value of x we can plot it into Equation 2

4x - y = -2

4(0.5) - y = -2

2 - y = -2

2 + 2 = y

y = 4

In summary, the solution of the simultaneous equations in (x, y) format results in (1/2, 4)

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