Answer :
To solve the simultaneous equations:
[tex]$ \left\{ \begin{array}{l} x + 6y = -19 \\ 5x + 4y = 9 \end{array} \right. $[/tex]
We can use the method of substitution or elimination. Let's use the elimination method. Here's a step-by-step solution:
1. Write the given equations clearly:
[tex]\[ \begin{aligned} &(1)\quad x + 6y = -19 \\ &(2)\quad 5x + 4y = 9 \\ \end{aligned} \][/tex]
2. Multiply Equation (1) by 5 to align the coefficient of \( x \) with Equation (2) for elimination:
[tex]\[ 5(x + 6y) = 5(-19) \][/tex]
Simplifying this gives us:
[tex]\[ 5x + 30y = -95 \quad (3) \][/tex]
3. Subtract Equation (2) from Equation (3) to eliminate \( x \):
[tex]\[ (5x + 30y) - (5x + 4y) = -95 - 9 \][/tex]
Simplifying the left-hand side (canceling \( 5x \)):
[tex]\[ 30y - 4y = -104 \][/tex]
Which reduces to:
[tex]\[ 26y = -104 \][/tex]
4. Solve for \( y \):
[tex]\[ y = \frac{-104}{26} = -4 \][/tex]
5. Substitute \( y = -4 \) into Equation (1) to find \( x \):
[tex]\[ x + 6(-4) = -19 \][/tex]
Simplifying this:
[tex]\[ x - 24 = -19 \][/tex]
So:
[tex]\[ x = -19 + 24 \][/tex]
Which gives:
[tex]\[ x = 5 \][/tex]
Therefore, the solution to the simultaneous equations is:
[tex]\[ x = 5 \quad \text{and} \quad y = -4 \][/tex]
[tex]$ \left\{ \begin{array}{l} x + 6y = -19 \\ 5x + 4y = 9 \end{array} \right. $[/tex]
We can use the method of substitution or elimination. Let's use the elimination method. Here's a step-by-step solution:
1. Write the given equations clearly:
[tex]\[ \begin{aligned} &(1)\quad x + 6y = -19 \\ &(2)\quad 5x + 4y = 9 \\ \end{aligned} \][/tex]
2. Multiply Equation (1) by 5 to align the coefficient of \( x \) with Equation (2) for elimination:
[tex]\[ 5(x + 6y) = 5(-19) \][/tex]
Simplifying this gives us:
[tex]\[ 5x + 30y = -95 \quad (3) \][/tex]
3. Subtract Equation (2) from Equation (3) to eliminate \( x \):
[tex]\[ (5x + 30y) - (5x + 4y) = -95 - 9 \][/tex]
Simplifying the left-hand side (canceling \( 5x \)):
[tex]\[ 30y - 4y = -104 \][/tex]
Which reduces to:
[tex]\[ 26y = -104 \][/tex]
4. Solve for \( y \):
[tex]\[ y = \frac{-104}{26} = -4 \][/tex]
5. Substitute \( y = -4 \) into Equation (1) to find \( x \):
[tex]\[ x + 6(-4) = -19 \][/tex]
Simplifying this:
[tex]\[ x - 24 = -19 \][/tex]
So:
[tex]\[ x = -19 + 24 \][/tex]
Which gives:
[tex]\[ x = 5 \][/tex]
Therefore, the solution to the simultaneous equations is:
[tex]\[ x = 5 \quad \text{and} \quad y = -4 \][/tex]
