Question

8 solve this system of equations. show your work.$3x = 6y - 21$$6x - 9y = -30$$\frac{3x}{3}=\frac{6y}{3}-\frac{21}{3}$$x = 2y - 7$$6(2y - 7)-9y=-30$$12y - 42 - 9y=-30$solution290 lesson 13 solve systems of linear equations algebraically

Explanation:

Step1: Isolate $x$ in first equation

Divide $3x=6y-21$ by 3:
$$\frac{3x}{3}=\frac{6y}{3}-\frac{21}{3}$$
$$x=2y-7$$

Step2: Substitute $x$ into second equation

Replace $x$ in $6x-9y=-30$:
$$6(2y-7)-9y=-30$$

Step3: Expand and simplify the equation

$$12y-42-9y=-30$$
$$3y-42=-30$$

Step4: Solve for $y$

Add 42 to both sides, then divide by 3:
$$3y=-30+42$$
$$3y=12$$
$$y=\frac{12}{3}=4$$

Step5: Substitute $y$ to find $x$

Use $x=2y-7$:
$$x=2(4)-7=8-7=1$$

Answer:

$x=1$, $y=4$