Solve the system of equations. {:[8y-9x=-3],[5y-8x=10],[x=◻],[y=◻]:}

Write System of Equations: Write down the system of equations. We have the following system of equations: 8y - 9x = -3 5y - 8x = 10Solve for y: Solve the first equation for y. To isolate y, we can add 9x to both sides of the first equation and then divide by 8: 8y = 9x - 3 y = (9x - 3) / 8Substitute into Second Equation: Substitute the expression for y into the second equation. Substitute y = (9x - 3) / 8 into the second equation: 5((9x - 3) / 8) - 8x = 10Eliminate Fraction: Multiply both sides of the equation by 8 to eliminate the fraction. 8 * [5((9x - 3) / 8) - 8x] = 8 * 10 5(9x - 3) - 64x = 80Combine Like Terms: Distribute and combine like terms. 45x - 15 - 64x = 80 -19x - 15 = 80Isolate x Term: Add 15 to both sides to isolate the term with x. -19x - 15 + 15 = 80 + 15 -19x = 95Solve for x: Divide both sides by -19 to solve for x. x = 95 / -19 x = -5Substitute into y Expression: Substitute x = -5 into the expression for y. y = (9(-5) - 3) / 8 y = (-45 - 3) / 8 y = -48 / 8 y = -6

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations.

{:[8y-9x=-3],[5y-8x=10],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 8 y-9 x=-3 \\ 5 y-8 x=10 \\ x=\square \\ y=\square \end{array}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations using elimination

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l} 8 y-9 x=-3 \\ 5 y-8 x=10 \\ x=\square \\ y=\square \end{array}

Write System of Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $8y - 9x = -3$ $\newline$ $5y - 8x = 10$
Solve for y: Solve the first equation for y. $\newline$ To isolate y, we can add $9x$ to both sides of the first equation and then divide by $8$ : $\newline$ $8y = 9x - 3$ $\newline$ $y = \frac{9x - 3}{8}$
Substitute into Second Equation: Substitute the expression for $y$ into the second equation. $\newline$ Substitute $y = \frac{9x - 3}{8}$ into the second equation: $\newline$ $5\left(\frac{9x - 3}{8}\right) - 8x = 10$
Eliminate Fraction: Multiply both sides of the equation by $8$ to eliminate the fraction. $\newline$ $8 \times [5((9x - 3) / 8) - 8x] = 8 \times 10$ $\newline$ $5(9x - 3) - 64x = 80$
Combine Like Terms: Distribute and combine like terms. $\newline$ $45x - 15 - 64x = 80$ $\newline$ $-19x - 15 = 80$
Isolate x Term: Add $15$ to both sides to isolate the term with $x$ . $\newline$ $-19x - 15 + 15 = 80 + 15$ $\newline$ $-19x = 95$
Solve for x: Divide both sides by $-19$ to solve for x. $\newline$ $x = \frac{95}{-19}$ $\newline$ $x = -5$
Substitute into $y$ Expression: Substitute $x = -5$ into the expression for $y$ . $\newline$ $y = \frac{9(-5) - 3}{8}$ $\newline$ $y = \frac{-45 - 3}{8}$ $\newline$ $y = \frac{-48}{8}$ $\newline$ $y = -6$