Questions: Use substitution -5x + 2y = 13 y = 2x + 6 x= y=

Use substitution -5x + 2y = 13 y = 2x + 6 x= y=
Transcript text: Use substitution \[ \begin{aligned} -5 x+2 y & =13 \\ y & =2 x+6 \end{aligned} \] \[ \begin{array}{l} x= \\ y= \end{array} \] $\square$ $\square$
failed

Solution

failed
failed

Solution Steps

To solve the system of equations using substitution, we can follow these steps:

  1. Substitute the expression for \( y \) from the second equation into the first equation.
  2. Solve the resulting equation for \( x \).
  3. Substitute the value of \( x \) back into the second equation to find \( y \).
Step 1: Substitute \( y \) from the second equation into the first equation

Given the system of equations: \[ \begin{aligned} -5x + 2y &= 13 \\ y &= 2x + 6 \end{aligned} \] Substitute \( y = 2x + 6 \) into the first equation: \[ -5x + 2(2x + 6) = 13 \]

Step 2: Simplify and solve for \( x \)

Simplify the equation: \[ -5x + 4x + 12 = 13 \] Combine like terms: \[ -x + 12 = 13 \] Solve for \( x \): \[ -x = 1 \implies x = -1 \]

Step 3: Substitute \( x \) back into the second equation to find \( y \)

Substitute \( x = -1 \) into \( y = 2x + 6 \): \[ y = 2(-1) + 6 = 4 \]

Final Answer

\[ \boxed{x = -1} \] \[ \boxed{y = 4} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The image contains a graph or chart-like representation drawn with blue lines on a grid background. The shape resembles a 'W' or zig-zag pattern with multiple line segments connected at points.
failedAnswered
Convert the following decimals to percents. 0.008=0.8 % 0.31=31.0 % 9.1=910.0 % 0.05=
failedAnswered
A variable is: Select one: a. a statement of association. b. a factor that always remains constant. c. a fact given a definition in a research process. d. anything that can change. e. a testable statement about the relationship between two or more hypotheses.
failedAnswered
where the road became a bridge over a dry riverbed, tangled with brush and clinging vines; the bridge of rustic logs, made for trysting, but virginal and untested by lovers; on up the road, past the buildings, with the southern verandas half-a-cityblock long, to the sudden forking, barren of buildings, birds, or grass, where the road turned off to the insane asylum. I always come this far and open my eyes. The spell breaks and I try to re-see the rabbits, so tame through having never been hunted, that played in the hedges and along the road. And I see the purple and silver of thistle growing between the broken glass and sunheated stones, the ants moving nervously in single file, and I turn and retrace my steps and come back to the winding road past the hospital, where at night in certain wards the gay student nurses dispensed a far more precious thing than pills to lucky boys in the know; and I come to a stop at the chapel. And then it is suddenly winter, with the moon high above and the chimes in the steeple ringing and a sonorous choir of trombones rendering a Christmas carol; and over all is a quietness and an ache as though all the world were loneliness. And I stand and listen beneath the high-hung moon, hearing "A Mighty Fortress Is Our God," majestically mellow on four trombones, and then the organ. The sound floats over all, clear like the night, liquid, serene, and lonely. And I stand as for an answer and see in my mind's eye the cabins surrounded by empty fields beyond red clay roads, and beyond a certain road a river, sluggish and covered with algae more yellow than green in its stagnant stillness; past more empty fields, to the sun-shrunk shacks at the railroad crossing where the disabled veterans visited the whores, hobbling down the tracks on crutches and canes; sometimes pushing the legless, thighless one in a red wheelchair. And sometimes I listen to hear if music reaches that far, but recall only the drunken laughter of sad, sad whores. And I stand in the circle where three roads
failedAnswered
For the function g whose graph is shown, find a number a that satisfies the given description. (a) The limit of g(x) as x approaches a does not exist but g(a) is defined. a=2 (b) The limit of g(x) as x approaches a exists but g(a) is not defined. a= (c) The limit of g(x) as x approaches a from the left and the limit of g(x) as x approaches a from the right both exist but the limit of g(x) as x approaches a does not exist. smaller value a= larger value a= (d) The limit of g(x) as x approaches a from the right equals g(a) but the limit of g(x) as x approaches a from the left does not equal g(a). a=