To solve the given system of equations, we need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations. The system of equations is:
[tex]\[
\begin{aligned}
&1.\quad 5x + 2y = 7 \\
&2.\quad -2x + 6y = 9
\end{aligned}
\][/tex]
Step-by-Step Solution:
1. Express [tex]\(x\)[/tex] or [tex]\(y\)[/tex] in terms of the other variable from one of the equations.
Let's start by solving the first equation for [tex]\(x\)[/tex]:
[tex]\[
5x + 2y = 7 \implies 5x = 7 - 2y \implies x = \frac{7 - 2y}{5}
\][/tex]
2. Substitute this expression into the second equation.
Substitute [tex]\(x = \frac{7 - 2y}{5}\)[/tex] into [tex]\(-2x + 6y = 9\)[/tex]:
[tex]\[
-2\left(\frac{7 - 2y}{5}\right) + 6y = 9
\][/tex]
Simplify this equation:
[tex]\[
-\frac{2(7 - 2y)}{5} + 6y = 9 \implies -\frac{14 - 4y}{5} + 6y = 9
\][/tex]
Multiply through by 5 to eliminate the fractions:
[tex]\[
-14 + 4y + 30y = 45
\][/tex]
Combine like terms:
[tex]\[
34y - 14 = 45
\][/tex]
Solve for [tex]\(y\)[/tex]:
[tex]\[
34y = 59 \implies y = \frac{59}{34} \implies y \approx 1.735
\][/tex]
3. Round [tex]\(y\)[/tex] to the nearest tenth.
Thus, the [tex]\(y\)[/tex]-coordinate of the solution, rounded to the nearest tenth, is:
[tex]\[
y \approx 1.7
\][/tex]
Therefore, the [tex]\(y\)[/tex]-coordinate of the solution is [tex]\(1.7\)[/tex].
