Question

1. $-\frac{5}{7} - \frac{11}{7}x = -y$

$2y = 7 + 5x$

Explanation:

Step1: Simplify first equation

Multiply the first equation \(-\frac{5}{7} - \frac{11}{7}x = -y\) by \(-1\) to get \(y=\frac{5}{7}+\frac{11}{7}x\).

Step2: Substitute y into second equation

Substitute \(y = \frac{5}{7}+\frac{11}{7}x\) into \(2y = 7 + 5x\). So \(2(\frac{5}{7}+\frac{11}{7}x)=7 + 5x\).

Step3: Expand left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(2\times\frac{5}{7}+2\times\frac{11}{7}x=7 + 5x\), which is \(\frac{10}{7}+\frac{22}{7}x=7 + 5x\).

Step4: Eliminate fractions

Multiply every term by 7 to get \(10 + 22x=49 + 35x\).

Step5: Solve for x

Subtract \(22x\) from both sides: \(10=49 + 13x\). Then subtract 49 from both sides: \(13x=10 - 49=-39\). Divide both sides by 13: \(x=- 3\).

Step6: Solve for y

Substitute \(x = - 3\) into \(y=\frac{5}{7}+\frac{11}{7}x\). \(y=\frac{5}{7}+\frac{11}{7}\times(-3)=\frac{5-33}{7}=\frac{-28}{7}=-4\).

Answer:

\(x=-3,y = - 4\)