Question

question 4 solve the following system of equations with the substitution method: $\begin{cases}-5x - 4y=-53\\-x + 2y=-5end{cases}$ answer: ( , ) enter your answers as integers or as reduced fractions in the form a/b.

Explanation:

Step1: Solve the second - equation for x

From $-x + 2y=-5$, we get $x = 2y + 5$.

Step2: Substitute x into the first equation

Substitute $x = 2y+5$ into $-5x-4y=-53$. Then $-5(2y + 5)-4y=-53$.
Expand the left - hand side: $-10y-25 - 4y=-53$.
Combine like terms: $-14y-25=-53$.
Add 25 to both sides: $-14y=-53 + 25=-28$.
Divide both sides by - 14: $y = 2$.

Step3: Find the value of x

Substitute $y = 2$ into $x = 2y+5$. Then $x=2\times2 + 5=9$.

Answer:

$(9,2)$