Answer :
To solve the given system of linear equations:
[tex]\[ \begin{array}{l} 5x + 2y = 22 \\ -2x + 6y = 3 \end{array} \][/tex]
we can use the substitution or elimination method. Here, the elimination method can be particularly effective. Follow these steps to find the solution:
1. First equation:
[tex]\[ 5x + 2y = 22 \][/tex]
2. Second equation:
[tex]\[ -2x + 6y = 3 \][/tex]
For elimination, align the equations to eliminate one of the variables.
3. Multiply the first equation by 3 to align the coefficients of [tex]\( y \)[/tex] in both equations:
[tex]\[ 3(5x + 2y) = 3(22) \][/tex]
This simplifies to:
[tex]\[ 15x + 6y = 66 \][/tex]
4. Now, we have:
[tex]\[ \begin{array}{l} 15x + 6y = 66 \\ -2x + 6y = 3 \end{array} \][/tex]
5. Eliminate [tex]\( y \)[/tex] by subtracting the second equation from the first:
[tex]\[ (15x + 6y) - (-2x + 6y) = 66 - 3 \][/tex]
Simplifying this, we get:
[tex]\[ 15x + 6y + 2x - 6y = 63 \][/tex]
[tex]\[ 17x = 63 \][/tex]
6. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{63}{17} \][/tex]
7. Convert this to a decimal and round to the nearest tenth:
[tex]\[ x \approx 3.7 \][/tex]
So, the [tex]\( x \)[/tex]-coordinate of the solution is:
[tex]\[ \boxed{3.7} \][/tex]
[tex]\[ \begin{array}{l} 5x + 2y = 22 \\ -2x + 6y = 3 \end{array} \][/tex]
we can use the substitution or elimination method. Here, the elimination method can be particularly effective. Follow these steps to find the solution:
1. First equation:
[tex]\[ 5x + 2y = 22 \][/tex]
2. Second equation:
[tex]\[ -2x + 6y = 3 \][/tex]
For elimination, align the equations to eliminate one of the variables.
3. Multiply the first equation by 3 to align the coefficients of [tex]\( y \)[/tex] in both equations:
[tex]\[ 3(5x + 2y) = 3(22) \][/tex]
This simplifies to:
[tex]\[ 15x + 6y = 66 \][/tex]
4. Now, we have:
[tex]\[ \begin{array}{l} 15x + 6y = 66 \\ -2x + 6y = 3 \end{array} \][/tex]
5. Eliminate [tex]\( y \)[/tex] by subtracting the second equation from the first:
[tex]\[ (15x + 6y) - (-2x + 6y) = 66 - 3 \][/tex]
Simplifying this, we get:
[tex]\[ 15x + 6y + 2x - 6y = 63 \][/tex]
[tex]\[ 17x = 63 \][/tex]
6. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{63}{17} \][/tex]
7. Convert this to a decimal and round to the nearest tenth:
[tex]\[ x \approx 3.7 \][/tex]
So, the [tex]\( x \)[/tex]-coordinate of the solution is:
[tex]\[ \boxed{3.7} \][/tex]
