### Home > CCA > Chapter 4 > Lesson 4.2.4 > Problem4-71

4-71.

Solve these systems of equations using any method. Check each solution, if possible.

1.  \begin{aligned} [t] 2x + 3y = 9 \quad \; \, \\ -3x + 3y = -6 \end{aligned}

• One strategy to solve this system of equations is to multiply the bottom equation by $-1$ so you can eliminate.

$2x+3y=9$
$3x-3y=6$
$5x=15$

After finding $x$, plug in its value into one of the equations to find the value of $y$.

$x=3$
$y=1$

1.  \begin{aligned}[t] x = 8 - 2y \\ y - x = 4 \; \; \end{aligned}

• Because one of the equations above is already solved for $x$, one strategy to solve this system is to substitute the first equation in for $x$ in the second equation.

1.  \begin{aligned}[t] y = -\frac{1}{2}x + 7 \\ y = x - 8 \quad \; \; \, \end{aligned}

• Use the Equal Values Method.

1.  \begin{aligned}[t] 9x + 10y = 14 \\ 7x + 5y = -3 \, \end{aligned}

• Refer to part (a).

$x=-4;y=5$