Question

question 2 of 10
solve the following system of
solution. round your answer to
$5x + 2y = 7$
$- 2x + 6y = 9$

Explanation:

Step1: Eliminate one variable

We can use the elimination method. First, multiply the first equation \(5x + 2y = 7\) by 3 to make the coefficients of \(y\) in both equations have a common multiple.
\(3\times(5x + 2y)=3\times7\)
\(15x + 6y = 21\)

Step2: Subtract the second equation

Now we have the two equations:
\(15x + 6y = 21\) (from Step 1)
\(-2x + 6y = 9\) (original second equation)

Subtract the second equation from the first equation:
\((15x + 6y)-(-2x + 6y)=21 - 9\)
\(15x + 6y + 2x - 6y = 12\)
\(17x = 12\)

Step3: Solve for \(x\)

Divide both sides of the equation \(17x = 12\) by 17:
\(x=\frac{12}{17}\approx0.7059\)

Step4: Substitute \(x\) into one of the original equations to solve for \(y\)

Substitute \(x = \frac{12}{17}\) into the first original equation \(5x + 2y = 7\):
\(5\times\frac{12}{17}+2y = 7\)
\(\frac{60}{17}+2y = 7\)
Subtract \(\frac{60}{17}\) from both sides:
\(2y = 7-\frac{60}{17}\)
\(2y=\frac{119 - 60}{17}\)
\(2y=\frac{59}{17}\)
Divide both sides by 2:
\(y=\frac{59}{34}\approx1.7353\)

Answer:

\(x\approx0.71\), \(y\approx1.74\) (rounded to two decimal places)