Question

lindsay wrote the system shown below.
-3x + 5y = 21
6x - y = -15
remember -\frac{a}{b}=slope
and \frac{c}{b}=y - intercept
(2,27)
(2,0)
(-2,3)
(-3,-3)

Explanation:

Step1: Rearrange the first equation for y

Starting with \(-3x + 5y=21\), add \(3x\) to both sides: \(5y = 3x + 21\). Then divide by 5: \(y=\frac{3}{5}x+\frac{21}{5}\).

Step2: Rearrange the second equation for y

Starting with \(6x - y=-15\), subtract \(6x\) from both sides: \(-y=-6x - 15\). Multiply by - 1: \(y = 6x+15\).

Step3: Use the substitution method

Set the two - equations equal to each other: \(\frac{3}{5}x+\frac{21}{5}=6x + 15\). Multiply through by 5 to clear the fraction: \(3x+21 = 30x+75\).

Step4: Solve for x

Subtract \(3x\) from both sides: \(21=27x + 75\). Then subtract 75 from both sides: \(27x=21 - 75=-54\). Divide by 27: \(x=-2\).

Step5: Solve for y

Substitute \(x = - 2\) into \(y = 6x+15\). So \(y=6\times(-2)+15=-12 + 15 = 3\).

Answer:

\((-2,3)\)